stability of peakons the peakons are peaked solitary wave solutions of a certain nonlinear dispersive equation that is a model in shallow water theory and the theory of hyperelastic rods we give a very simple proof of the orbital stability of the peakons in the h1 norm 2000 john wiley sons inc

a note on well posedness for camassa holm equation in this note we investigate the problem of well posedness for a shallow water equation with data having critical regularity our results are based on the use of besov spaces b2 rs which generalize the sobolev spaces hs with critical index s 3 2

on the cauchy problem for the two component camassa holm system in this paper we establish the local well posedness for the two component camassa holm system in a range of the besov spaces we also derive a wave breaking mechanism for strong solutions in addition we determine the exact blow up rate of such solutions to the system

global solutions and blow up phenomena to a shallow water equation abstract a nonlinear shallow water equation which includes the famous camassa holm ch and degasperis procesi dp equations as special cases is investigated the local well posedness of solutions for the nonlinear equation in the sobolev space h s r with s 3 2 is developed provided that 1 x 2 u 0 does not change sign u 0 h s s 3 2 and u 0 l 1 r the existence and uniqueness of the global solutions to the equation are shown to be true in u t x c 0 h s r c 1 0 h s 1 r conditions that lead to the development of singularities in finite time for the solutions are also acquired

the steiglitz mcbride identification algorithm revisited convergence analysis and accuracy aspects the convergence and accuracy properties of the steiglitz and mcbride identification method are examined the analysis is valid for a sufficiently large number of data it is shown that the method can converge to the true parameter vector only when the additive output noise is white in that case the method is proved to be locally convergent to the true parameters the global convergence properties are also investigated it is pointed out that the method is not always globally convergent some sufficient conditions guaranteeing global convergence are given assuming convergence takes place the estimates are shown to be asymptotically gaussian distributed an explicit expression is given for their asymptotic covariance matrix

the camassa holm equation as a geodesic flow on the diffeomorphism group misiolek j geom phys 24 203 208 1998 has shown that the camassa holm equation is a geodesic flow on the bott virasoro group in this paper it is shown that the camassa holm equation for the case 0 is the geodesic spray of the weak riemannian metric on the diffeomorphism group of the line or the circle obtained by right translating the h1 inner product over the entire group this paper uses the right trivialization technique to rigorously verify that the euler poincare theory for lie groups can be applied to diffeomorphism groups the observation made in this paper has led to physically meaningful generalizations of the ch equation to higher dimensional manifolds

on a shallow water model with the coriolis effect abstract in the present study an asymptotic model for wave propagation in shallow water with the effect of the coriolis force is derived from the governing equation in two dimensional flows the transport equation theory is then applied to investigate the local well posedness and wave breaking phenomena for this model the nonexistence of the camassa holm type peaked solution and classification of various traveling wave solutions to the new system are also established moreover it is shown that all the symmetric waves to this model are traveling waves

null controllability of the structurally damped wave equation with moving control we investigate the internal controllability of the wave equation with structural damping on the one dimensional torus we assume that the control is acting on a moving point or on a moving small interval with a constant velocity we prove that the null controllability holds in some suitable sobolev space and after a fixed positive time independent of the initial conditions

on the wave breaking phenomena for the periodic two component dullin gottwald holm system abstract considered herein is the well posedness problem of the periodic two component dullin gottwald holm dgh system on the circle which can be derived from euler s equation with constant vorticity in shallow water waves moving over a linear shear flow the result of blow up solutions for certain initial profiles in a manner which corresponds to wave breaking is established

brief paper enforcing stability constraints in set membership identification of linear dynamic systems in this paper we consider the identification of linear systems a priori known to be stable from input output data corrupted by bounded noise by taking explicitly into account a priori information on system stability a formal definition of the feasible parameter set for a stable linear system is provided on the basis of a detailed analysis of the geometrical structure of the feasible set convex relaxation techniques are presented to solve nonconvex optimization problems arising in the computation of parameter uncertainty intervals properties of the computed relaxed bounds are discussed a simulated example is presented to show the effectiveness of the proposed technique

on the controllability of the linearized benjamin bona mahony equation we study the boundary controllability properties of the linearized benjamin bona mahony equation left begin array ll u t u xxt u x 0 x in 0 1 t 0 u t 0 0 u 1 t f t t 0 end array right we show that the equation is approximately controllable but not spectrally controllable no finite linear combination of eigenfunctions other than zero is controllable next we prove a finite controllability result and we estimate the norms of the controls needed in this case

a semi analytical integration method for j2 flow theory of plasticity with linear isotropic hardening abstract in this paper an exact time integration scheme is presented for von mises elastoplasticity with linear isotropic hardening at small deformations the method is based on the constant strain rate assumption which is widely accepted in displacement based finite element applications the deviatoric form of the rate equation using the method proposed by krieg and krieg in r d krieg d b krieg accuracies of numerical solution methods for the elastic perfectly plastic model j press vess technol trans asme 99 1977 510 515 is rewritten to a system of nonlinear odes with two scalar functions the radius of the mises circle and an angle obtained by using the scalar product of the stress deviator and the strain rate the time integration of these functions gives an exact solution in implicit form using the incomplete beta function in addition by the exact linearization of this new semi analytical solution a stress updating algorithm and the consistent tangent operator are derived the numerical performance and accuracy of the proposed method are illustrated on numerical examples moreover a comparison of the proposed method with the well known radial return method is included

analytical cpp in energy mapped stress space application to a modified drucker prager yield surface in conventional stress space the closest point projection cpp of computational plasticity in general does not provide the closest point in a euclidean sense but rather in an energy metric as an alternative this contribution discusses an energy mapped stress space such that cpp is indeed the closest point in a strict euclidean sense this perspective clarifies which yield surfaces can be handled analytically analytical solutions are possible if the cpp can be expressed as a polynomial of order 4 or less this is demonstrated by means of a modified drucker prager yield surface in which the hydrostatic tensile apex is removed through the use of hyperbolic meridians

traveling wave solutions of the camassa holm equation all weak traveling wave solutions of the camassa holm equation are classified we show that in addition to smooth solutions there are a multitude of traveling waves with singularities peakons cuspons stumpons and composite waves

asymptotic stabilizability by stationary feedback of the two dimensional euler equation the multiconnected case we construct a feedback law which allows us to asymptotically stabilize the euler system for incompressible inviscid fluids in two dimensions in the case of a multiconnected bounded domain by means of a control localized on a part of the boundary that meets every connected component of the boundary this generalizes a result of coron siam j control optim 37 1999 pp 1874 1896 concerning simply connected domains

on the controllability of the vlasov poisson system in this paper we study the controllability of the vlasov poisson system in a periodic domain by means of an interior control located in an spatial subdomain the first result proves the local exact zero controllability in the two dimensional torus between two small acceptable distribution functions with an arbitrary control zone a second result establishes the global exact controllability in arbitrary dimension provided the control zone satisfies the condition that it contains a hyperplane of the torus

algorithmic issues for three invariant hyperplastic critical state models implicit stress integration and the consistent tangents are presented for critical state hyperplasticity models which include a dependence on the third invariant of stress an elliptical deviatoric yielding criterion 43 is incorporated within the family of geotechnical models first proposed by collins and hilder 8 an alternative expression for the yield function is proposed and the consequences of different forms of that function are revealed in terms of the stability and efficiency of the stress return algorithm errors associated with the integration scheme are presented it is shown how calibration of the two new material constants is achieved through examining one dimesional consolidation tests and undrained triaxial compression data material point simulations of drained triaxial compression tests are then compared with established experimental results strain probe analyses are used to demonstrate the concepts of energy dissipation and stored plastic work along with the robustness of the integration method over twenty finite element boundary value problems are then simulated these include single three dimensional element tests plane strain footing analyses and cavity expansion tests the rapid convergence of the global newton raphson procedure using the consistent tangent is demonstrated in small strain and finite deformation simulations

reuleaux plasticity analytical backward euler stress integration and consistent tangent analytical backward euler stress integration is presented for a deviatoric yielding criterion based on a modified reuleaux triangle the criterion is applied to a cone model which allows control over the shape of the deviatoric section independent of the internal friction angle on the compression meridian the return strategy and consistent tangent are fully defined for all three regions of principal stress space in which elastic trial states may lie errors associated with the integration scheme are reported these are shown to be less than 3 for the case examined run time analysis reveals a 2 5 5 0 times speed up at a material point over the iterative newton raphson backward euler stress return scheme two finite element analyses are presented demonstrating the speed benefits of adopting this new formulation in larger boundary value problems the simple modified reuleaux surface provides an advance over mohr coulomb and drucker prager yield envelopes in that it incorporates dependencies on both the lode angle and intermediate principal stress without incurring the run time penalties of more sophisticated models

exact boundary controllability for the linear korteweg de vries equation on the half line this paper is concerned with the controllability of the linear korteweg de vries equation on the domain o 0 infty the control being applied at the left endpoint x 0 it is shown that the em exact boundary controllability holds true in l 2 0 infty provided that the solutions are not required to be in l infty 0 t l 2 0 infty the proof rests on a carleman s estimate and an approximation theorem a similar result is obtained for the heat equation and for the schrodinger equation

on the global existence and wave breaking criteria for the two component camassa holm system considered herein is a two component camassa holm system modeling shallow water waves moving over a linear shear flow a wave breaking criterion for strong solutions is determined in the lowest sobolev space hs s 32 by using the localization analysis in the transport equation theory moreover an improved result of global solutions with only a nonzero initial profile of the free surface component of the system is established in this sobolev space hs

on the blow up rate and the blow up set of breaking waves for a shallow water equation we consider the problem of the development of singularities for classical solutions to a new periodic shallow water equation blow up can occur only in the form of wave breaking i e the solution remains bounded but its slope becomes unbounded in finite time a quite detailed description of the wave breaking phenomenon is given there is at least a point in general depending on time where the slope becomes infinite exactly at breaking time the precise blow up rate is established and for a large class of initial data we also determine the blow up set

generalized hunter saxton equation and the geometry of the group of circle diffeomorphisms we study an equation lying mid way between the periodic hunter saxton and camassa holm equations and which describes evolution of rotators in liquid crystals with external magnetic field and self interaction we prove that it is an euler equation on the diffeomorphism group of the circle corresponding to a natural right invariant sobolev metric we show that the equation is bihamiltonian and admits both cusped and smooth traveling wave solutions which are natural candidates for solitons we also prove that it is locally well posed and establish results on the lifespan of its solutions throughout the paper we argue that despite similarities to the kdv ch and hs equations the new equation manifests several distinctive features that set it apart from the other three

autonomous ovsyannikov theorem and applications to nonlocal evolution equations and systems abstract this work presents an ovsyannikov type theorem for an autonomous abstract cauchy problem in a scale of decreasing banach spaces which in addition to existence and uniqueness of solution provides an estimate about the analytic lifespan of the solution then using this theorem it studies the cauchy problem for camassa holm type equations and systems with initial data in spaces of analytic functions on both the circle and the line which is the main goal of this paper finally it studies the continuity of the data to solution map in spaces of analytic functions

design of simple low order finite elements for large strain analysis of nearly incompressible solids a simple four node quadrilateral and an eight node hexahedron for large strain analysis of nearly incompressible solids are proposed based on the concept of deviatoric volumetric split and the replacement of the compatible deformation gradient with an assumed modified counterpart the formulation developed is applicable to arbitrary material models the closed form of the corresponding exact tangent stiffnesses which have a particularly simple structure is derived it ensures asymptotically quadratic rates of convergence of the newton raphson scheme employed in the solution of the implicit finite element equilibrium equations from a practical point of view the incorporation of the proposed elements into existing codes is straightforward it requires only small changes in the routines of the standard displacement based 4 node quadrilateral and 8 node brick a comprehensive set of numerical examples involving hyperelasticity as well as multiplicative elasto plasticity is provided it illustrates the performance of the proposed elements over a wide range of applications including strain localisation problems metal forming simulation and adaptive analysis

the cauchy problem of a periodic 2 component μ hunter saxton system in besov spaces abstract this paper is concerned with the local well posedness and the precise blow up scenario for a periodic 2 component hunter saxton system in besov spaces moreover we state a new global existence result to the system our obtained results for the system improve considerably earlier results

consistent tangent operators for rate independent elastoplasticity abstract it is shown that for problems involving rate constitutive equations such as rate independent elastoplasticity the notion of consistency between the tangent stiffness operator and the integration algorithm employed in the solution of the incremental problem plays a crucial role in preserving the quadratic rate of asymptotic convergence of iterative solution schemes based upon newton s method within the framework of closest point projection algorithms a methodology is presented whereby tangent operators consistent with this class of algorithms may be systematically developed to wit associative j 2 flow rules with general nonlinear kinematic and isotropic hardening rules as well as a class of non associative flow rules are considered the resulting iterative solution scheme preserves the asymptotic quadratic convergence characteristic of newton s method whereas use of the socalled elastoplastic tangent in conjunction with a radial return integration algorithm a procedure often employed results in newton type of algorithms with suboptimal rate of convergence application is made to a set of numerical examples which include saturation hardening laws of exponential type

geodesic flows on semidirect product lie groups geometry of singular measure valued solutions the epdiff equation or dispersionless camassa holm equation in 1d is a well known example of geodesic motion on the diff group of smooth invertible maps diffeomorphisms its recent two component extension governs geodesic motion on the semidirect product mathrm diff circleds mathcal f where mathcal f denotes the space of scalar functions this paper generalizes the second construction to consider geodesic motion on mathrm diff circleds mathfrak g where mathfrak g denotes the space of scalar functions that take values on a certain lie algebra for example mathfrak g mathcal f otimes mathfrak so 3 measure valued delta like solutions are shown to be momentum maps possessing a dual pair structure thereby extending previous results for the epdiff equation the collective hamiltonians are shown to fit into the kaluza klein theory of particles in a yang mills field and these formulations are shown to apply also at the continuum pde level in the continuum description the kaluza klein approach produces the kelvin circulation theorem

holder continuity for a modified camassa holm system this paper is concerned with the holder continuity for a modified camassa holm system we show that the date to solution for the modified camassa holm system is holder continuous from bounded set of sobolev spaces with exponent s 3 2 measured in a weaker sobolev norm with index r s on the line our result also holds for the periodic case

exact boundary controllability of the korteweg de vries equation we consider boundary control of the distributed parameter system described by the korteweg de vries kdv equation posed on a finite interval alpha leq x leq beta left begin array l u t u x uu x u xxx 0 u alpha t h 1 t qquad u beta t h 2 t qquad u x beta t h 3 t u end array right qquad for t geq 0 it is shown that by choosing appropriate control inputs h j t j 1 2 3 one can always guide the system from a given initial state phi in h s alpha beta to a given terminal state psi in h s alpha beta in the time period 0 t so long as phi and psi satisfy phi cdot w cdot 0 h s alpha beta leq delta quad mbox and quad psi cdot w cdot t h s alpha beta leq delta for some delta 0 independent of phi and psi where s geq 0 and w equiv w x t is a given smooth solution of the kdv equation this exact boundary controllability is established by considering a related initial value control problem of the kdv equation posed on the whole line r various recently discovered smoothing properties of the kdv equation have played important roles in our approach

qualitative analysis for the new shallow water model with cubic nonlinearity abstract considered in this paper is the new shallow water model with cubic nonlinearity which admits the single peaked solitons and multi peakon solutions and includes both the modified camassa holm equation also called fokas olver rosenau qiao equation and the novikov equation as two special cases the main investigation is the cauchy problem of the new shallow water model with qualitative properties of its solutions we first establish the local well posedness for the cauchy problem of the new shallow water model and then derive a precise blow up scenario and the blow up mechanisms for solutions with certain initial profiles moreover with analytic initial data we show that its solutions are analytic in both variables globally in space and locally in time finally we investigate the persistence properties of the solution to the cauchy problem of the new shallow water model

non associated reuleaux plasticity analytical stress integration and consistent tangent for finite deformation mechanics analytical backward euler stress integration is presented for a volumetrically non associated pressure sensitive yield criterion based on a modified reuleaux triangle this advances previous work on associated reuleaux plasticity using energy mapped stress space the analytical solution is 2 4 times faster than a standard numerical backward euler algorithm the merit in transforming to and operating in this space is that the stress return is truly the closest point on the surface to the elastic trial state the paper includes a tension cut off formed by a second cone and describes the steps necessary to allow the model s incorporation within a finite deformation framework finite element results show a 59 runtime saving for a modified reuleaux model over a willam warnke cone giving comparable accuracy in a thick walled cylinder expansion problem the consistent tangent provides asymptotically quadratic convergence in the newton raphson scheme under both i small strain infinitesimal deformation and ii large strain finite deformation finite element simulations it is shown that the introduction of non associated flow changes the plastic deformation field and reduces the heave predicted in a plane strain rigid strip footing problem the proposed model offers a significant improvement over the drucker prager and mohr coulomb formulations by better reproducing the material dependence on the lode angle and intermediate principal stress at little extra computational effort

initial boundary value problem and asymptotic stabilization of the camassa holm equation on an interval abstract we investigate the nonhomogeneous initial boundary value problem for the camassa holm equation on an interval we provide a local in time existence theorem and a weak strong uniqueness result next we establish a result on the global asymptotic stabilization problem by means of a boundary feedback law

exact boundary controllability of the korteweg de vries equation around a non trivial stationary solution the exact boundary controllability of the non linear korteweg de vries equation on bounded domains is studied only the first spatial derivative at the right endpoint is assumed to be controlled in this case the exact controllability has been shown by rosier 1997 when the length l of the domain is not in the set n

exact controllability of a nonlinear korteweg de vries equation on a critical spatial domain we consider the boundary controllability problem for a nonlinear korteweg de vries equation with the dirichlet boundary condition we study this problem for a spatial domain with a critical length for which the linearized control system is not controllable in order to deal with the nonlinearity we use a power series expansion of second order we prove that the nonlinear term gives the local exact controllability around the origin provided that the time of control is large enough

rapid non linear finite element analysis of continuous and discontinuous galerkin methods in matlab matlab is adept at the development of concise finite element fe routines however it is commonly perceived to be too inefficient for high fidelity analysis this paper aims to challenge this preconception by presenting two optimised fe codes for both continuous galerkin cg and discontinuous galerkin dg methods although this has previously been achieved for linear elastic problems no such optimised matlab script currently exists which includes the effects of material non linearity to incorporate these elasto plastic effects the externally applied load is split into a discrete number of loadsteps equilibrium is determined at each loadstep between the externally applied load and the arising internal forces using the newton raphson method the optimisation of the scripts is primarily achieved using vectorised blocking algorithms which minimise ram to cache overheads and maximise cache reuse the optimised codes yielded maximum speed gains of 25 7 and 10 1 when compared to the corresponding unoptimised scripts for cg and dg respectively it was identified that with increasing refinement of the mesh the solver time begins to dominate the overall simulation time this bottleneck has a greater disadvantage on the dg code predominantly due the asymmetric nature of the global stiffness matrix the implementation of an efficient solver would see further improvement to the overall run times particularly for large problems

well posedness and blow up solutions for an integrable nonlinearly dispersive model wave equation abstract we establish local well posedness in the sobolev space hs with any s 3 2 for an integrable nonlinearly dispersive wave equation arising as a model for shallow water waves known as the camassa holm equation however unlike the more familiar korteweg devries model we demonstrate conditions on the initial data that lead to finite time blow up of certain solutions

optimal distributed controls of a class of nonlinear dispersive equations with cubic nonlinearity abstract this paper is devoted to the optimal distributed control problem governed by a class of nonlinear dispersive equations with cubic nonlinearity which contains the famous novikov equation as special case we first investigate the existence and uniqueness of the weak solution for the controlled system and then find an optimal solution for the controlled system with the generalized cost functional moreover by means of the method suggested by a ya dubovitskii and a a milyutin we establish the first order necessary optimality condition of optimal control for the controlled system in the fixed final horizon case

improved explicit integration in plasticity the article presents a simple but efficient numerical scheme for the integration of non linear constitutive equations in which the principal reason for the inaccuracy of the classical explicit schemes for example forward euler scheme is effectively eliminated in the newly developed explicit scheme where there is no need for iteration the implementation simplicity of the forward euler scheme and accuracy of the approach which is using the backward euler scheme to integrate the constitutive equations are successfully combined computational performance of the proposed next increment corrects error nice integration scheme particularly regarding the accuracy and the cpu time consumption is first analysed on a case of complex loading of a material point when comparing it to the forward euler backward euler trapezoidal and midpoint integration schemes it turns out that because of its capability of a fast and relatively accurate integration of the constitutive equations the nice scheme is very convenient for the integration of constitutive models where a direct solution technique is used to solve a boundary value problem although the deduction of the new integration scheme is general its implementation for shell applications needs particular care namely in order to satisfy the zero normal stress condition during the whole integration a through thickness strain increment has to be adequately chosen in each integration step the nice scheme which was also implemented into abaqus explicit via user material subroutine vumat interface platform has been additionally compared with the abaqus explicit default integration scheme backward euler and forward euler scheme two loading case studies namely the bending of a square plate and the stretching of a specimen including the onset of necking are considered with two constitutive models the von mises and gtn material model being adopted generally the nice scheme has demonstrated to be advantageous in cases where reasonable accuracy and very fast integration of the constitutive model is demanded which is mostly the case in engineering computations with a direct solution method for example explicit dynamics and metal forming process simulations copyright 2009 john wiley sons ltd

the curvature of semidirect product groups associated with two component hunter saxton systems in this paper we study two component versions of the periodic hunter saxton equation and its variant considering both equations as a geodesic flow on the semidirect product of the circle diffeomorphism group with a space of scalar functions on we show that both equations are locally well posed the main result of this paper is that the sectional curvature associated with the 2hs is constant and positive and that 2 hs allows for a large subspace of positive sectional curvature the issues of this paper are related to some of the results for 2ch and 2dp presented in escher et al 2011 j geom phys 61 436 52

on the cauchy problem for a two component degasperis procesi system abstract this paper is concerned with the cauchy problem for a two component degasperis procesi system firstly the local well posedness for this system in the nonhomogeneous besov spaces is established then the precise blow up scenario for strong solutions to the system is derived finally two new blow up criterions and the exact blow up rate of strong solutions to the system are presented

some properties of solutions to the periodic two component hyperelastic rod wave equation abstract in this paper we study the cauchy problem of the periodic two component hyperelastic rod wave equation we first establish the local well posedness and precise blow up scenario then we obtain several blow up results and the blowup rate of strong solutions moreover we present two global existence results for strong solutions finally we consider analyticity of solutions and the initial boundary value problem

on the blow up structure for the generalized periodic camassa holm and degasperis procesi equations considered herein are the generalized camassa holm and degasperis procesi equations in the spatially periodic setting the precise blow up scenarios of strong solutions are derived for both of equations several conditions on the initial data guaranteeing the development of singularities in finite time for strong solutions of these two equations are established the exact blow up rates are also determined finally geometric descriptions of these two integrable equations from non stretching invariant curve flows in centro equiaffine geometries pseudo spherical surfaces and affine surfaces are given

controllability and asymptotic stabilization of the camassa holm equation we investigate the problems of exact controllability and asymptotic stabilization of the camassa holm equation on the circle by means of a distributed control the results are global and in particular the control prevents the solution from blowing up

global solutions to a special case of the generalized weakly dissipative periodic two component camassa holm system abstract we establish global well posedness to the generalized weakly dissipative periodic two component camassa holm system in some special case

nurbs plasticity yield surface representation and implicit stress integration for isotropic inelasticity in numerical analysis the failure of engineering materials is controlled through specifying yield envelopes or surfaces that bound the allowable stress in the material however each surface is distinct and requires a specific equation describing the shape of the surface to be formulated in each case these equations impact on the numerical implementation specifically relating to stress integration of the models and therefore a separate algorithm must be constructed for each model this paper presents for the first time a way to construct yield surfaces using techniques from non uniform rational basis spline nurbs surfaces such that any isotropic convex yield envelope can be represented within the same framework these surfaces are combined with an implicit backward euler type stress integration algorithm to provide a flexible numerical framework for computational plasticity the algorithm is inherently stable as the iterative process starts and remains on the yield surface throughout the stress integration the performance of the algorithm is explored using both material point investigations and boundary value analyses demonstrating that the framework can be applied to a variety of plasticity models

on the cauchy problem for the modified novikov equation with peakon solutions abstract a new nonlinear dispersive partial differential equation with cubic nonlinearity which includes the famous novikov equation as special case is investigated we first establish the local well posedness in a range of the besov spaces b p r s p r 1 s max 3 2 1 1 p but s 2 1 p which generalize the sobolev spaces h s well posedness in h s with s 3 2 is also established by applying kato s semigroup theory then we give the precise blow up scenario moreover with analytic initial data we show that its solutions are analytic in both variables globally in space and locally in time finally we prove that peakon solutions to the equation are global weak solutions

global existence for a new periodic integrable equation we establish the local well posedness for a new periodic integrable equation we show that the equation has classical solutions that blowup in finite time as well as classical solutions which exist globally in time

unique continuation property and control for the benjamin bona mahony equation on a periodic domain abstract we consider the benjamin bona mahony bbm equation on the one dimensional torus t r 2 z we prove a unique continuation property ucp for small data in h 1 t with nonnegative zero means next we extend the ucp to certain bbm like equations including the equal width wave equation and the kdv bbm equation applications to the stabilization of the above equations are given in particular we show that when an internal control acting on a moving interval is applied in the bbm equation then a semiglobal exponential stabilization can be derived in h s t for any s 1 furthermore we prove that the bbm equation with a moving control is also locally exactly controllable in h s t for any s 0 and globally exactly controllable in h s t for any s 1 in a sufficiently large time depending on the h s norms of the initial and terminal states

global conservative solutions of the camassa holm equation this paper develops a new approach in the analysis of the camassa holm equation by introducing a new set of independent and dependent variables the equation is transformed into a semilinear system whose solutions are obtained as fixed points of a contractive transformation these new variables resolve all singularities due to possible wave breaking returning to the original variables we obtain a semigroup of global solutions depending continuously on the initial data our solutions are conservative in the sense that the total energy equals a constant for almost every time

well posedness and analyticity for the cauchy problem for the generalized camassa holm equation abstract in this paper we are concerned with the cauchy problem for the generalized camassa holm equation which was proposed by hakkaev and kirchev s hakkaev k kirchev local well posedness and orbital stability of solitary wave solutions for the generalized camassa holm equation comm partial differential equations 30 2005 761 781 we establish the local well posedness for a range of besov spaces moreover with analytic initial data we show that its solutions are analytic in both variables globally in space and locally in time which extends some results of danchin r danchin a few remarks on the camassa holm equation differential integral equations 14 2001 953 988 and himonas and misiolek a himonas g misiolek analyticity of the cauchy problem for an integrable evolution equation math ann 327 2003 575 584 to more general equations

global existence and blow up phenomena for a weakly dissipative periodic 2 component camassa holm system we first establish local well posedness for a weakly dissipative periodic 2 component camassa holm system we then present two global existence results for strong solutions to the equation we finally obtain several blow up results and the blow up rate of strong solutions to the equation

on the stability of dynamic models obtained by least squares identification the stability properties of the least squares ls models fitted to stochastic dynamic systems described by difference equations are investigated it is shown through a counterexample that the ls method can for such systems give unstable models sufficient conditions for the stability of the ls models in question are also included

well posedness of the cauchy problem for a shallow water equation on the circle in this paper we consider the periodic cauchy problem for a fifth order modification of the camassa holm equation we prove local well posedness in appropriate bourgain spaces for initial data in a sobolev space hs t s 1 2 we also prove global well posedness for data in h1 t and of arbitrary size the proofs are based on a priori estimates using fourier analysis techniques microlocalization in phase space an interpolation argument and a fixed point theorem

exact controllability of scalar conservation laws with an additional control in the context of entropy solutions in this paper we study the exact controllability problem for nonlinear scalar conservation laws on a compact interval with a regular convex flux and in the framework of entropy solutions with the boundary data and a source term depending only on the time as controls we provide sufficient conditions for a state to be reachable in arbitrary small time to do so we introduce a slightly modified wave front tracking algorithm

on the weak solutions to a shallow water equation we obtain the existence of global in time weak solutions to the cauchy problem for a one dimensional shallow water equation that is formally integrable and can be obtained by approximating directly the hamiltonian for euler s equation in the shallow water regime the solution is obtained as a limit of viscous approximation the key elements in our analysis are some new a priori one sided supernorm and space time higher norm estimates on the first order derivatives 2000 john wiley sons inc

an unbiased equation error identifier and reduced order approximations the equation error ee identification technique is modified to remove the parameter bias problem induced by uncorrelated measurement errors the modification replaces a monic constraint with a unit norm constraint the asymptotic solution replaces a normal equation with an eigenequation the resulting algorithm is simpler than previous schemes while at the same time preserving the desirable properties of the conventional ee method simplicity of an on line algorithm unimodality of the performance surface and consistent identification in the sufficient order case in the more realistic undermodeled case a robustness result shows that the mean optimal parameter values of both the monic and unit norm ee schemes correspond to a stable transfer function for all degrees of undermodeling and for all stationary output disturbances provided the input sequence satisfies an autoregressive constraint otherwise an unstable model may result model approximation properties for the undermodeled case are exposed in detail for the case of autoregressive inputs although both the monic and unit norm variants provide pade approximation properties the unit norm version is capable of autocorrelation matching properties as as well and yields the optimal solution to a first and second order interpolation problem finally the mismodeling error for the undermodeled case is shown to be a well behaved function of the hankel singular values of the unknown system this modification allows ee methods to be admitted to the class of unbiased identification and approximation techniques

on a camassa holm type equation with two dependent variables we consider a generalization of the camassa holm ch equation with two dependent variables called ch2 introduced in a paper by liu and zhang liu s q and zhang y 2005 j geom phys 54 427 53 we briefly provide an alternative derivation of it based on the theory of hamiltonian structures on the dual of a lie algebra the lie algebra involved here is the same algebra as underlies the nls hierarchy we study the structural properties of the hierarchy defined by the ch2 equation within the bi hamiltonian theory of integrable pdes and provide its lax representation then we explicitly discuss how to construct classes of solutions both of peakon and of algebro geometrical type finally we sketch the construction of a class of singular solutions defined by setting to zero one of the two dependent variables

on the cauchy problem of a periodic 2 component μ hunter saxton system abstract in this paper we study the cauchy problem of a periodic 2 component hunter saxton system we first establish the local well posedness for the periodic 2 component hunter saxton system by kato s semigroup theory then we derive the precise blow up scenario for strong solutions to the system moreover we present some blow up results for strong solutions to the system finally we give a global existence result to the system

controllability and stabilizability of the third order linear dispersion equation on a periodic domain in this paper solutions of the third order linear dispersion equations frac partial w partial t frac partial 3 w partial x 3 f x t qquad text and qquad frac partial w partial t frac partial 3 w partial x 3 0 are studied for t geqq 0 0 leqq x leqq 2 pi in the first case periodic boundary conditions are imposed at 0 and 2 pi and the distributed control f which may however have support smaller than 0 2 pi is assumed to be generated by a linear feedback law conserving the volume int 0 2 pi w x t dx while monotonically reducing int 0 2 pi w x t 2 dx for the second equation a feedback boundary control having the same properties is applied in both cases uniform exponential decay to a constant state is obtained related exact controllability questions are also studied and affirmative results are obtained

blow up phenomena for the weakly dissipative dullin gottwald holm equation revisited in this paper we investigate the cauchy problem for the weakly dissipative dullin gottwald holm equation we first establish the local well posedness result by kato s semigroup theory then we obtain the precise blow up scenario and present some blow up results for strong solutions to the equation finally we discuss the blow up rate of the wave breaking solutions this result complements the early one in the literature such as novruzov j math phys 54 092703 2013

the trajectories of particles in stokes waves analyzing a free boundary problem for harmonic functions we show that there are no closed particle paths in an irrotational inviscid traveling wave propagating at the surface of water over a flat bed within a period each particle experiences a backward forward motion with a slight forward drift

identification of multivariable stochastic linear systems via spectral analysis given time domain data estimation of the parametric multiple input multiple output mimo infinite impulse response transfer function given time domain input output io data is considered we first propose a frequency domain solution to the least squares equation error multivariable system identification problem using the power spectrum and the cross spectrum of the io data to estimate the io parametric transfer function the proposed approach is shown to yield a unimodal performance surface and consistent identification in colored noise and the sufficient order case we then investigate an iterative pseudo maximum likelihood approach and analyze its consistency under sufficient order modeling finally a computer simulation example is provided to illustrate the two approaches

on the null asymptotic stabilization of the two dimensional incompressible euler equations in a simply connected domain we study the asymptotic stabilization of the origin for the two dimensional 2 d euler equation of incompressible inviscid fluid in a bounded domain we assume that the controls act on an arbitrarily small nonempty open subset of the boundary we prove the null global asymptotic stabilizability by means of explicit feedback laws if the domain is connected and simply connected

nurbs plasticity yield surface evolution and implicit stress integration for isotropic hardening this paper extends the non uniform rational basis spline nurbs plasticity framework of coombs et al 2016 to include isotropic hardening of the yield surfaces the approach allows any smooth isotropic yield envelope to be represented by a nurbs surface the key extension provided by this paper is that the yield surface can expand or contract through the movement of control points linked to the level of inelastic straining experienced by the material the model is integrated using a fully implicit backward euler algorithm that constrains the return path to the yield surface and allows the derivation of the algorithmic consistent tangent to ensure optimum convergence of the global equilibrium equations this provides a powerful framework for elasto plastic constitutive models where unlike the majority of models presented in the literature the underlying numerical algorithm and implemented code remains unchanged for different yield surfaces the performance of the algorithm is demonstrated and validated using both material point and boundary values simulations including plane stress plane strain and three dimensional examples for different yield criteria

exact controllability and stabilizability of the korteweg de vries equation in this paper we consider distributed control of the system described by the korteweg de vries equation i atu uaxu e3 u f on the interval 0 0 with periodic boundary conditions ii au 27r t ku o t k 0 1 2 where the distributed control f f x t is restricted so that the volume f u x t dx of the solution is conserved both exact controllability and stabilizibility questions are studied for the system in the case of open loop control if the control f is allowed to act on the whole spatial domain 0 27r it is shown that the system is globally exactly controllable i e for given t 0 and functions q x x with the same volume one can alway find a control f so that the system i ii has a solution u x t satisfying u x 0 0 x u x t x if the control f is allowed to act on only a small subset of the domain 0 27r then the same result still holds if the initial and terminal states b and 0 have small amplitude in a certain sense in the case of closed loop control the distributed control f is assumed to be generated by a linear feedback law conserving the volume while monotonically reducing f u x t 2dx the solutions of the resulting closed loop system are shown to have uniform exponential decay to a constant state as in the open loop control case a small amplitude assumption is needed if the control is allowed to act on only a small subdomain the smoothing property of the periodic linear kdv equation discovered recently by bourgain has played an important role in establishing the exact controllability and stabilizability results presented in this paper

a new exact integration method for the drucker prager elastoplastic model with linear isotropic hardening abstract this paper presents the exact stress solution of the non associative drucker prager elastoplastic model governed by linear isotropic hardening rule the stress integration is performed under constant strain rate assumption and the derived formulas are valid in the setting of small strain elastoplasticity theory based on the time continuous stress solution a complete discretized stress updating algorithm is also presented providing the solutions for the special cases when the initial stress state is located in the apex and when the increment produces a stress path through the apex explicit expression for the algorithmically consistent tangent tensor is also derived in addition a fully analytical strain solution is also derived for the stress driven case using constant stress rate assumption in order to get a deeper understanding of the features of these solutions two numerical test examples are also presented

the local well posedness and existence of weak solutions for a generalized camassa holm equation abstract a generalization of the camassa holm equation a model for shallow water waves is investigated using the pseudoparabolic regularization technique its local well posedness in sobolev space h s r with s 3 2 is established via a limiting procedure in addition a sufficient condition for the existence of weak solutions of the equation in lower order sobolev space h s with 1 s 3 2 is developed

symplectic structures their backlund transformations and hereditary symmetries abstract it is shown that compatible symplectic structures lead in a natural way to hereditary symmetries we recall that a hereditary symmetry is an operator valued function which immediately yields a hierarchy of evolution equations each having infinitely many commuting symmetries all generated by this hereditary symmetry furthermore this hereditary symmetry usually describes completely the soliton structure and the conservation laws of these equations this result then provide us with a method for constructing hereditary symmetries and hence exactly solvable evolution equations in addition we show how symplectic structures transform under backlund transformations this leads to a method for generating a whole class of symplectic structures from a given one several examples and applications are given illustrating the above results also the connection of our results with those of gelfand and dikii and of magri is briefly pointed out

optimal solution and optimality condition of the hunter saxton equation this paper is devoted to the optimal distributed control problem governed by the hunter saxton equation with constraints on the control we first investigate the existence and uniqueness of weak solution for the controlled system with appropriate initial value and boundary conditions in contrast with our previous research the proof of solution mapping is local lipschitz continuous which is one big improvement second based on the well posedness result we find a unique optimal control and optimal solution for the controlled system with the quadratic cost functional moreover we establish the sufficient and necessary optimality condition of an optimal control by means of the optimal control theory not limited to the necessary condition which is another major novelty of this paper we also discuss the optimality conditions corresponding to two physical meaningful distributed observation cases

identification of linear systems via spectral analysis given time domain data consistency reduced order approximation and performance analysis estimation of a parametric input output i o infinite impulse response transfer function given time domain i o data is considered some of the desirable properties of any approach to this problem are unimodality of the performance surface consistent identification in the sufficient order case and stability of the fitted model under undermodeling we first consider a frequency domain solution to the least squares equation error identification problem using the power spectrum and the cross spectrum of the i o data to estimate the i o parametric transfer function the proposed approach is shown to yield a unimodal performance surface consistent identification in colored noise and sufficient order case and stable fitted models under undermodeling for arbitrary stationary inputs so long as they are persistently exciting of sufficiently high order asymptotic performance analysis is carried out for both sufficient order and reduced order cases these asymptotic results are then used to derive statistics on the corresponding estimated transfer function we also investigate an iterative pseudomaximum likelihood approach and analyze its performance under sufficient order modeling finally computer simulation examples are provided to illustrate the two approaches

on the inverse spectral problem for the camassa holm equation abstract a key basis for seeking periodic solutions of the camassa holm equation is to understand the associated spectral problem y 1 4 y my the periodic spectrum can be recovered from the norming constants and the elements of the auxiliary spectrum the potential can then be reconstructed from the periodic spectrum a necessary and sufficient condition for exponential decrease of the widths 2n 2n 1for a sequence 0 m c1 r

optimal control of a class of nonlocal dispersive equations abstract in this paper the optimal control problem for a class of nonlocal dispersive equations is considered we introduce a kind of the definition of a weak solution to this equation and prove the existence of a unique weak solution in a special hilbert space s 0 t we also discuss the existence of optimal control solution to a class of nonlocal dispersive equations with the cost functional adopting the dubovitskii milyutin functional analytical approach we prove the necessary optimality condition of optimal control local maximum principle for the investigative system in fixed final horizon case

a class of mixed assumed strain methods and the method of incompatible modes a three field mixed formulation in terms of displacements stresses and an enhanced strain field is presented which encompasses as a particular case the classical method of incompatible modes within this frame work incompatible elements arise as particular compatible mixed approximations of the enhanced strain field the conditions that the stress interpolation contain piece wise constant functions and be l2 ortho gonal to the enhanced strain interpolation ensure satisfaction of the patch test and allow the elimination of the stress field from the formulation the preceding conditions are formulated in a form particularly convenient for element design as an illustration of the methodology three new elements are developed and shown to exhibit good performance a plane 3d elastic plastic quad an axisymmetric element and a thick plate bending quad the formulation described herein is suitable for non linear analysis

integrable evolution equations on spaces of tensor densities and their peakon solutions we study a family of equations defined on the space of tensor densities of weight on the circle and introduce two integrable pde one of the equations turns out to be closely related to the inviscid burgers equation while the other has not been identified in any form before we present their lax pair formulations and describe their bihamiltonian structures we prove local wellposedness of the corresponding cauchy problem and include results on blow up as well as global existence of solutions moreover we construct peakon and multi peakon solutions for all 0 1 and shock peakons for 3 we argue that there is a natural geometric framework for these equations that includes other well known integrable equations and which is based on v arnold s approach to euler equations on lie groups