feedback boundary control of linear hyperbolic systems with relaxation we consider boundary stabilization for one dimensional systems of linear hyperbolic partial differential equations with relaxation structure such equations appear in many applications by combining weighted lyapunov functions the structure is used to derive new stabilization results the result is illustrated with an application to boundary stabilization of water flows in open canals

normal forms and quadratic nonlinear klein gordon equations on construit une transformation qui change l equation a non linearite cubique que l on sait resoudre a 3 1 dimensions on demontre que la solution du probleme original a le meme comportement asymptotique que l equation de klein gordon non lineaire

3d symplectic expansion for piezoelectric media the symplectic series expansion method is extended to three dimensional problem for transversely isotropic piezoelectric media the governing equations are first derived in hamiltonian form and symplectic eigensolutions are directly obtained through analytical method all solutions of the problem are reduced to finding eigenvalues and eigensolutions the classical st venant solutions are described by zero eigensolutions and the localized solutions are depicted by non zero eigensolutions symplectic relationships of the ortho normalization are used end conditions are rewritten by eigensolutions and a numerical scheme is formed analytically some numerical examples are given copyright 2007 john wiley sons ltd

optimal control of cell mass and maturity in a model of follicular ovulation in this paper we study optimal control problems associated with a scalar hyperbolic conservation law modeling the development of ovarian follicles changes in the age and maturity of follicular cells are described by a two dimensional conservation law where the control terms act on the velocities the control problem consists in optimizing the follicular cell resources so that the follicular maturity reaches a maximal value in fixed time formulating the optimal control problem within a hybrid framework we prove necessary optimality conditions in the form of the hybrid maximum principle then we derive the optimal strategy and show that there exists at least one optimal bang bang control with one single switching time

feedback boundary control of linear hyperbolic equations with stiff source term abstractwe consider feedback boundary control of hyperbolic systems with stiff source terms by combining weighted lyapunov functions the structure is used to derive stabilisation results in our analysis we give stabilising feedback laws that allow a robust uniform exponential stabilisation for a whole range of values of an uncertain parameter with a decay rate that is independent of the parameter in particular we are interested in the limit case when the relaxation parameter approaches zero the result is illustrated with the numerical analysis on the decay rate of the lyapunov function in terms of the stiff parameter and an application to boundary stabilisation of gas dynamics in pipes

three dimensional static analysis of multi layered piezoelectric hollow spheres via the state space method a general non axisymmetric exact analysis of the statics of a laminated piezoelectric hollow sphere is presented in the paper by using a state space method to select a proper set of state variables three displacement functions and two stress functions are introduced it is found that the basic equations of a spherically isotropic piezoelectric medium are eventually turned to two separated state equations with constant coefficients the solutions of which are then obtained by virtue of matrix theory the continuity conditions at each interface are then used to derive two relationships between respective boundary variables at the inner and outer spherical surfaces no matter how many layers the sphere contains the orders of the final solving equations remain unaltered

transient response of a hollow cylinder with radial and axial material inhomogeneity the transient response of a hollow finite cylinder with radial and axial material inhomogeneity to a pulse of short duration is analyzed the problem is solved in two steps radial inhomogeneity is treated first by dividing the cylinder into coaxial segments each with a constant modulus e which is allowed to vary from segment to segment transfer matrices relating variables at the two radial interfaces of a segment combine to satisfy continuity of stress and displacement at these interfaces the galerkin method is then utilized to treat the general case with both radial and axial inhomogeneity adopting the eigenfunctions of the radially inhomogeneous cylinder as trial functions features of both static and transient responses resemble that for a weakening material along the axis displacement increases and stress reduces in proportion to the reduction in modulus spatial attenuation of transient stress cannot be replicated when geometric dimensionality is reduced from 3 d axisymmetric to 2 d plane strain

exact boundary controllability for 1 d quasilinear hyperbolic systems with a vanishing characteristic speed the general theory on exact boundary controllability for general first order quasilinear hyperbolic systems requires that the characteristic speeds of the system do not vanish this paper deals with exact boundary controllability when this is not the case some important models are also shown as applications of the main result the strategy uses the return method which allows one in certain situations to recover nonzero characteristic speeds

free vibration of laminated circular piezoelectric plates and discs the free vibration characteristics of laminated circular piezoelectric plates and discs are considered using a discrete layer model of the weak form of the equations of periodic motion through thickness approximations are used for the three displacement components and the electrostatic potential resulting in an accurate representation of the discontinuity in gradients of these quantities from the mismatch in material properties at a dissimilar interface in the radial and circumferential co ordinates several different approximation functions are used that depend upon the type of problem being considered specifically the boundary conditions at the outer edge of the solid representative cases are studied both for thin plates and for thick discs excellent agreement is found with results of previous studies and several new results are presented

on the fundamental equations of electromagnetoelastic media in variational form with an application to shell laminae equations abstract the fundamental equations of elasticity with extensions to electromagnetic effects are expressed in differential form for a regular region of materials and the uniqueness of solutions is examined alternatively the fundamental equations are stated as the euler lagrange equations of a unified variational principle which operates on all the field variables the variational principle is deduced from a general principle of physics by modifying it through an involutory transformation then a system of two dimensional shear deformation equations is derived in differential and fully variational forms for the high frequency waves and vibrations of a functionally graded shell also a theorem is given which states the conditions sufficient for the uniqueness in solutions of the shell equations on the basis of a discrete layer modeling the governing equations are obtained for the motions of a curved laminae made of any numbers of functionally graded distinct layers whenever the displacements and the electric and magnetic potentials of a layer are taken to vary linearly across its thickness the resulting equations in differential and fully variational invariant forms account for various types of waves and coupled vibrations of one and two dimensional structural elements as well the invariant form makes it possible to express the equations in a particular coordinate system most suitable to the geometry of shell plate or laminae the results are shown to be compatible with and to recover some of earlier equations of plane and curved elements for special material geometry and or effects

alternative state space formulations for magnetoelectric thermoelasticity with transverse isotropy and the application to bending analysis of nonhomogeneous plates abstract by introducing two displacement functions and two stress functions the governing equations of the linear theory of magneto electro thermo elasticity with transverse isotropy are simplified on selecting certain physical quantities as the basic unknowns two new state equations are established each of them is order reduced when compared with the one reported recently in literature leading to a higher numerical efficiency the material inhomogeneity along the axis of symmetry z direction can be taken into account and an approximate laminate model is employed to facilitate deriving analytical solutions the validity of new formulations is examined by considering a laminated magneto electro elastic rectangular plate and good agreement is obtained with existent results a plate with a functionally graded property is then analyzed the effect of magnetoelectric coupling in a batio3 cofe2o4 composite predicted from the micromechanics simulation is studied quantitatively

state vector approach to analysis of multilayered magneto electro elastic plates abstract the state vector equations for three dimensional orthotropic and linearly magneto electro elastic media are derived from the governing equations by eliminating x y xy b x b y d x and d y an efficient method is presented for analysis of multilayered magneto electro elastic plates the methodology is based on the mixed formulation in which basic unknowns are formed by collecting not only displacements electrical potential and magnetic potential but also some of stresses electrical displacements and magnetic induction as special case simply supported and multilayered rectangular plate is analyzed under the surface loading numerical results are presented graphically the procedure of numerical calculation shows that the formulation presented here is simple and direct

dynamic solution of a multilayered orthotropic piezoelectric hollow cylinder for axisymmetric plane strain problems the dynamic solution of a multilayered orthotropic piezoelectric infinite hollow cylinder in the state of axisymmetric plane strain is obtained by the method of superposition the solution is divided into two parts one is quasi static and the other is dynamic the quasi static part is derived by the state space method and the dynamic part is obtained by the separation of variables method coupled with the initial parameter method as well as the orthogonal expansion technique by using the obtained quasi static and dynamic parts and the electric boundary conditions as well as the electric continuity conditions a volterra integral equation of the second kind with respect to a function of time is derived which can be solved successfully by means of the interpolation method the displacements stresses and electric potentials are finally obtained the present method is suitable for a multilayered orthotropic piezoelectric infinite hollow cylinder consisting of arbitrary layers and subjected to arbitrary axisymmetric dynamic loads numerical results are finally presented and discussed

boundary controllability between sub and supercritical flow there are several studies of the boundary controllability of quasi linear hyperbolic systems where it is assumed that the eigenvalues of the system matrixdo not change their signs during the controlled process in this paper we consider the flow through a frictionless horizontal rectangular channel that is governed by de st venant equations and show that the state can be controlled in finite time from a stationary initial state to a given stationary terminal state in such a way that during this transition the state stays in the class of c 1 functions so in particular no shocks occur there is no restriction on the initial and terminal state so in some cases it is necessary that one or both eigenvalues of the system matrixchange the sign during the process various different cases occur control between subcritical states control between supercritical states transition from a subcritical to a supercritical state and transition from a supercritical to a subcritical state in the last two cases of a control between states of a different type one eigenvalue of the system matrixchanges its sign during the process when this happens at a boundary point during the process it is necessary to switch the type of boundary conditions we show how to construct controls where at each boundary at most one such switching is necessary

well posedness of the good boussinesq equation in analytic gevrey spaces and time regularity abstract the cauchy problem for the good boussinesq equation with data in analytic gevrey spaces on the line and the circle is considered and its local well posedness in these spaces is proved the proof is based on bilinear estimates in bourgain type spaces incorporating the symbol of the linear part of the equation and an exponential weight expressing the analytic gevrey regularity of the solution in the spatial variable also gevrey regularity of the solution in time variable is provided

free vibration studies of simply supported non homogeneous functionally graded magneto electro elastic finite cylindrical shells in this article free vibration studies on functionally graded materials fgm magneto electro elastic cylindrical shells have been carried out a series solution is assumed in circumferential and axial direction such that the three dimensional character of the solution is preserved the finite element model is derived based on constitutive equation of magneto electro elastic material accounting for coupling between elasticity electric and magnetic effect frequency behavior with the variation of power law index is analyzed and explained on the basis of constitutive material one of the aims of the study is to evaluate the influence of magnetic and piezoelectric effect on the structural frequency in addition influence of length to radius ratio and radius to thickness ratio on the frequency behaviour of such shells have been attempted

on linearized coupling conditions for a class of isentropic multiphase drift flux models at pipe to pipe intersections in this paper a general drift flux model describing a subsonic and isentropic multi phase fluid in connected pipes is considered each phase is assumed to be isentropic with its own sonic speed the components are gamma law gases with 1 for such a computational challenge at a junction is the computation of rarefaction waves which do not have a readily available analytical form firstly the well posedness of the riemann problem at the junction is discussed it is suggested that rarefaction waves should be linearized in order to obtain a more efficient numerical method for coupling such multi component flow some computational results on the dynamics of the multi phase gas in the pipes demonstrate the qualitative behavior of this approach

free vibration of simply supported functionally graded and layered magneto electro elastic plates by finite element method in this article free vibration studies on functionally graded anisotropic and linear magneto electro elastic plates have been carried out by semi analytical finite element method a series solution is assumed in the plane of the plate and finite element procedure is adopted across the thickness of the plate such a way that the three dimensional 3 d character of the solution is preserved the finite element model is derived based on constitutive equation of magneto electro elastic material accounting for coupling between elasticity electric and magnetic effect the present finite element is modeled with displacement components electric potential and magnetic potential as nodal degree of freedom the functionally graded material is assumed to be exponential in the thickness direction the numerical results obtained by the present model are in good agreement with the isotropic 3 d exact benchmark solutions available in literature numerical study includes the influence of the different exponential factor magneto electro elastic properties and effect of mechanical and electrical type of loading on induced magneto electro elastic fields further study has been carried out on higher harmonic study has been extended on functionally graded and layered magneto electro elastic plate

low regularity solutions of non homogeneous boundary value problems of a higher order boussinesq equation in a quarter plane abstract in this article we study an initial boundary value problem of the sixth order boussinesq equation on a half line with nonhomogeneous boundary conditions u t t u x x u x x x x u x x x x x x u 2 x x 0 x 0 t 0 u x 0 x u t x 0 x x 0 u 0 t h 1 t u x x 0 t h 2 t u x x x x 0 t h 3 t t 0 where 1 it is shown that the problem is locally well posed in c r l o c h s r with initial condition h s r h s 1 r and boundary condition h 1 h 2 h 3 in the product space h s 1 3 r h s 1 3 r h s 3 3 r for 1 2 s 0

on free vibration of non homogeneous transversely isotropic magneto electro elastic plates two independent state equations are established for transversely isotropic magneto electro elastic media by introducing proper stress and displacement functions the free vibration problem of simply supported rectangular plates with general inhomogeneous functionally graded material properties along the thickness direction is then considered an approximate laminate model is employed to transform the state equations with variable coefficients to the ones with constant coefficients two different classes of vibrations are found in particular the frequency of the first class is only related to the elastic property of the plate while that of the second class is affected by the couplings among the elastic electric and magnetic fields numerical results are presented and some important issues are discussed

free vibrations of functionally graded piezoceramic hollow spheres with radial polarization by introducing displacement functions as well as stress functions two independent state equations with variable coefficients are established from the three dimensional equations of a radially inhomogeneous spherically isotropic piezoelastic medium by virtue of the laminated approximation method the state equations are then transformed into the ones with constant variables in each layer and the state variable solutions are presented based on the solutions linear algebraic equations about the state variables only at the inner and outer spherical surfaces are derived by utilizing the continuity conditions at each interface frequency equations corresponding to two independent classes of vibrations are finally obtained from the free surface conditions numerical calculations are presented and the effect of the material gradient index on natural frequencies is discussed

sharp well posedness and ill posedness results for a quadratic non linear schrodinger equation abstract we establish that the quadratic non linear schrodinger equation iu t u xx u 2 where u r r c is locally well posed in h s r when s 1 and ill posed when s 1 previous work in c kenig g ponce l vega quadratic forms for the 1 d semilinear schrodinger equation trans amer math soc 346 1996 3323 3353 had established local well posedness for s 3 4 the local well posedness is achieved by an iteration using a modification of the standard x s b spaces the ill posedness uses an abstract and general argument relying on the high to low frequency cascade present in the non linearity and a computation of the first non linear iterate

improved local well posedness for the periodic good boussinesq equation abstract we prove that the good boussinesq model is locally well posed in the space h h 2 3 8 in the proof we employ the method of normal forms which allows us to explicitly extract the rougher part of the solution while we show that the remainder is in the smoother space c 0 t h t min 1 3 1 2 thus we establish a smoothing effect of order min 1 2 1 2 for the nonlinear evolution this is new even in the previously considered cases 0 1 4

free vibrations of piezoelectric cylindrical shells filled with compressible fluid abstract three displacement functions are introduced to represent each mechanical displacement according to the three dimensional theory after expanding these functions and the electric potential with orthogonal series the free vibration equation of piezoelectric cylindrical shells satisfying ss3 edge conditions can be obtained the equation was solved by utilizing bessel functions with complex arguments the effects of compressible fluid on shells are considered and some new phenomena which are exclusive for piezoelectric cylindrical shells are reported results of empty infinite piezoelectric cylindrical shells are compared to those presented in relative references some lowest frequencies that were missed by paul and venkatesan paul h s and venkatesan m 1987 vibrations of hollow circular cylinder of piezoelectric ceramics journal of the acoustic society of america82 852 856 were discovered

ill posedness results for generalized boussinesq equations abstract in this article we investigate both the periodic and non periodic initial value problems for generalized boussinesq equations we show that the associated flow map is not smooth for a range of sobolev indices thus providing a threshold for the regularity needed to perform a picard iteration for these problems

a quadratic lyapunov function for saint venant equations with arbitrary friction and space varying slope the exponential stability problem of the nonlinear saint venant equations is addressed in this paper we consider the general case where an arbitrary friction and space varying slope are both included in the system which lead to non uniform steady states an explicit quadratic lyapunov function as a weighted function of a small perturbation of the steady states is constructed then we show that by a suitable choice of boundary feedback controls that we give explicitly the local exponential stability of the nonlinear saint venant equations for the h 2 norm is guaranteed

two exponential type integrators for the good boussinesq equation we introduce two exponential type integrators for the good boussinesq equation they are of orders one and two respectively and they require lower spatial regularity of the solution compared to classical exponential integrators for the first integrator we prove first order convergence in h r for solutions in h r 1 with r 1 2 this new integrator even converges with lower order in h r for solutions in h r i e without any additional smoothness assumptions for the second integrator we prove second order convergence in h r for solutions in h r 3 with r 1 2 and convergence in l 2 for solutions in h 3 numerical results are reported to illustrate the established error estimates the experiments clearly demonstrate that the new exponential type integrators are favorable over classical exponential integrators for initial data with low regularity

a note on the static behavior of simply supported laminated piezoelectric cylinders an exact three dimensional solution of the equations of linear piezoelectricity is given for the static response of a finite laminated piezoelectric cylinder with its ends simply supported the equilibrium equations and the conservation of charge equation are constructed in cylindrical coordinates the three displacement components and the electrostatic potential are expressed in terms of fourier series in the axial and circumferential directions leading to a coupled system of four ordinary differential equations in the radial coordinate the frobenious method is used to obtain the elastic and electric fields for each layer of the laminate which are a function of eight constants enforcing the boundary and continuity conditions across each interface yields the required number of equations to solve for these constants several examples are presented to study the fundamental behavior of these solids

well posedness and nonlinear smoothing for the good boussinesq equation on the half line abstract in this paper we study the regularity properties of the good boussinesq equation on the half line we obtain local existence uniqueness and continuous dependence on initial data in low regularity spaces moreover we prove that the nonlinear part of the solution on the half line is smoother than the initial data obtaining half derivative smoothing of the nonlinear term in some cases our paper improves the result in 17 being the first result that constructs solutions for the initial and boundary value problem of the good boussinesq equation below the l 2 space our theorems are sharp within the framework of the restricted norm method that we use and match the known results on the full line in 20 and 13

on the modelling and stabilization of flows in networks of open canals in this paper we present a model for the controlled flow of a fluid through a network of canals using a coupled system of st venant equations we then generalize in a variety of ways recent results of coron d andrea novel and bastin concerning the stabilizability around equilibrium of the flow through a single channel this work is based on the theory of quasilinear hyperbolic systems and in particular on a delicate result of li ta tsien concerning the existence and decay of global classical solutions

analysis and stabilization for networked linear hyperbolic systems of rationally dependent conservation laws in this paper for a networked linear hyperbolic partial differential equations pdes system of conservation laws the propagation periods of which are rationally dependent with coupled boundary conditions we propose a novel approach to analyze its controllability and observability in addition we propose a design method of a stabilizing controller where a boundary input with boundary valued feedback is considered first we characterize the control properties such as controllability of such a pde system in terms of the corresponding ones of a finite dimensional discrete time system defined on the boundaries of the pde system which is derived by fully exploiting the method of characteristics since the obtained discrete time system is low dimensional its analysis is relatively easier next we propose a design method of a stabilizing controller based on this discrete time system finally numerical simulations are presented to show that the proposed method is effective

gas flow in fan shaped networks classical solutions and feedback stabilization we analyze the subcritical gas flow through fan shaped networks of pipes that is through tree shaped networks with exactly one node where more than two pipes meet the gas flow in pipe networks is modeled by the isothermal euler equations a hyperbolic pde system of balance laws for this system we analyze stationary states and classical nonstationary solutions locally around a stationary state on a finite time interval furthermore we present a lyapunov function and boundary feedback laws to stabilize a fan shaped network around a given stationary state

time varying riemann solvers for conservation laws on networks abstract we consider a conservation law on a network and generic riemann solvers at nodes depending on parameters which can be seen as control functions assuming that the parameters have bounded variation as functions of time we prove existence of solutions to cauchy problems on the whole network

low regularity bilinear estimates for a quadratic nonlinear schrodinger equation abstract in this article we establish the bilinear estimates corresponding to the 1d and 2d nls with a quadratic nonlinearity c 1 u 2 c 2 u 2 which imply the local well posedness of the cauchy problem in h s for s 1 in the 1d case and for s 1 in the 2d case this is a continuation of our study n kishimoto local well posedness for the cauchy problem of the quadratic schrodinger equation with nonlinearity u 2 commun pure appl anal 7 2008 1123 1143 on the 1d nls with nonlinearity c u 2 previous papers by kenig ponce and vega and colliander delort kenig and staffilani established local well posedness for s 3 4 in 1d and in 2d respectively and when the nonlinearity is restricted to c u 2 papers by bejenaru and tao and bejenaru and de silva improved these results to s 1 in 1d and s 1 in 2d the bilinear estimate for 2d also yields an improvement on the growth rate of sobolev norms of finite energy global in time solutions to the 2d cubic nls

vibration of electro elastic versus magneto elastic circular annular plates using the chebyshev ritz method abstract the aim of this paper is to analyze three dimensional free vibration of magneto elastic electro elastic circular annular plates with different boundary conditions using the chebyshev ritz method in which a set of duplicate chebyshev polynomial series multiplied by the boundary function satisfying the boundary conditions are chosen as the trial functions of the displacement components the electric potential and the magnetic potential convergence of the method is checked using various chebyshev polynomial terms the effect of geometrical parameters and material properties of magneto elastic electro elastic circular annular plates on the eigenfrequencies of free vibration is considered

on the relaxation approximation of boundary control of the isothermal euler equations we consider the isothermal euler equations without friction that simulate gas flow through a pipe we consider the problem of boundary stabilisation of this system locally around a given stationary state we present a feedback law that is linear in the physical variables and yields exponential decay of the system state for the numerical solution of hyperbolic systems of conservation laws the jin xin relaxation scheme can be used therefore we also consider the boundary stabilisation of the relaxation system by the linear riemann feedback and present numerical examples that show the rapid exponential decay of the stabilised system

radial vibration of piezoelectric magnetostrictive composite hollow sphere the radial vibration of a multilayered piezoelectric magnetostrictive composite hollow sphere is investigated in terms of the gaussian equations two unknown time functions are first introduced to complete the solution of electric displacement and magnetic induction the solution for mechanical field involving two unknown time functions is obtained by means of the superposition method the state space method as well as the separation of variables method by means of the electric and magnetic boundary conditions and continuity conditions two volterra integral equations of the second kind with respect to two time functions are derived the interpolation method is employed to solve the volterra integral equations the present solution is suitable for analyzing the transient responses of composite hollow sphere composed of piezoelectric and magnetostrictive layers with arbitrary composite sequence numerical results are presented and discussed

quadratic forms for the 1 d semilinear schrodinger equation this paper is concerned with 1 d quadratic semilinear schr6dinger equations we study local well posedness in classical sobolev space hs of the associated initial value problem and periodic boundary value problem our main interest is to obtain the lowest value of s which guarantees the desired local well posedness result we prove that at least for the quadratic cases these values are negative and depend on the structure of the nonlinearity considered

global existence of smooth solutions and stability of solitary waves for a generalized boussinesq equation certain generalizations of one of the classical boussinesq type equations u tt u xx u 2 u xx xx are considered it is shown that the initial value problem for this type of equation is always locally well posed it is also determined that the special solitary wave solutions of these equations are nonlinearly stable for a range of their phase speeds these two facts lead to the conclusion that initial data lying relatively close to a stable solitary wave evolves into a global solution of these equations this contrasts with the results of blow up obtained recently by kalantarov and ladyzhenskaya for the same type of equation and casts additional light upon the results for the original version of this class of equations obtained via inverse scattering theory by deift tomei and trubowitz

the transient responses of piezoelectric hollow cylinders for axisymmetric plane strain problems by virtue of the separation of variables technique the axisymmetric plane strain electroelastic dynamic problem of hollow cylinder is transferred to an integral equation about a function with respect to time which can be solved successfully by means of the interpolation method then the solution of the displacements stresses electric displacements and electric potentials are finally obtained the present method is suitable for the hollow cylinder with arbitrary thickness subjected to arbitrary mechanical and electrical loads numerical results are also presented