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

existence of continuous solutions and stability for a general iterative functional equation in this paper c 0 solutions for a general form of iterative functional equation are considered when the coefficient of the first order iterate can be zero which is called the leading coefficient problem for polynomial like iterative equations moreover the stability of those c 0 solutions is also discussed finally as an application we give an algorithm to compute the piecewise linear solutions of polynomial like iterative equations

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

the set of all iterates is nowhere dense in c 0 1 0 1 we prove that if a mixing map f 0 1 0 1 belongs to the c 0 closure of the set of iterates and f 0 0 f 1 1 then f is an iterate itself together with some one dimensional techniques it implies that the set of all iterates is nowhere dense in c 0 1 0 1 giving the final answer to the question of a bruckner p humke and m laczkovich

steady periodic water waves with constant vorticity regularity and local bifurcation this paper studies periodic traveling gravity waves at the free surface of water in a flow of constant vorticity over a flat bed using conformal mappings the free boundary problem is transformed into a quasilinear pseudodifferential equation for a periodic function of one variable the new formulation leads to a regularity result and by use of bifurcation theory to the existence of waves of small amplitude even in the presence of stagnation points in the flow

error driven dynamical hp meshes with the discontinuous galerkin method for three dimensional wave propagation problems an hp adaptive discontinuous galerkin method for electromagnetic wave propagation phenomena in the time domain is proposed the method is highly efficient and allows for the first time the adaptive full wave simulation of large time dependent problems in three dimensional space refinement is performed anisotropically in the approximation order p and the mesh step size h regardless of the resulting level of hanging nodes for guiding the adaptation process a variant of the concept of reference solutions with largely reduced computational costs is proposed the computational mesh is adapted such that a given error tolerance is respected throughout the entire time domain simulation

forts of quadratic polynomials under iteration abstract since some dynamical behaviors of a one dimensional mapping are influenced by the number of forts attention is paid to the change of the number under iteration for simple computation we work on quadratic polynomials we use the theory of polynomial complete discrimination system to give a symbolic algorithm for the number of forts of iterated polynomials and apply the algorithm to quadratic functions which proves an alternative result that the number either persists to be 1 or tends to infinity under iteration we further compute the number for iterates of order 2 3 7 in the above infinity case and obtain critical values of the parameter at which the number changes those changes with finitely many data display a conjectured fibonacci rule

the hp local discontinuous galerkin method for low frequency time harmonic maxwell equations the local discontinuous galerkin method for the numerical approximation of the time harmonic maxwell equations in a low frequency regime is introduced and analyzed topologically nontrivial domains and heterogeneous media are considered containing both conducting and insulating materials the presented method involves discontinuous galerkin discretizations of the curl curl and grad div operators derived by introducing suitable auxiliary variables and so called numerical fluxes an hp analysis is carried out and error estimates that are optimal in the meshsize h and slightly suboptimal in the approximation degree p are obtained

fractional iterates for n dimensional maps this paper constitutes an extension of results of the paper by narayaninsamy int j bifurcations chaos 6 1 1996 55 67 we study here the solutions of the problem of the fractional iteration for n dimensional maps

local c 1 stability versus global c 1 unstability for iterative roots abstract stability of iterative roots is important in the numerical computation of iterative roots known results show that under some conditions iterative roots of strictly monotonic self mappings are c 0 stable in both the local sense and the global sense in this paper we discuss the c 1 stability for iterative roots of strictly increasing self mappings on a compact interval between two fixed points we prove that those iterative roots are locally c 1 stable but globally c 1 unstable

intuitive formulation of discontinuous galerkin surface integral equations for electromagnetic scattering problems an intuitive formulation of discontinuous galerkin surface integral equation dg sie method is proposed in this paper which is established by performing singularity extraction and singling out the infinitely large term in the entries of the impedance matrices associated with the sies which are popular in solving electromagnetic scattering problems nonoverlapping trial and test functions defined on triangles are employed without requirements of the surface current normal continuity across their internal boundary contours the proposed sie dg formulation is very flexible and is validated by examples of perfect electrically conducting targets in both conformal and nonconformal meshes

finite element study of the lorentz model in metamaterials metamaterials are materials with electromagnetic properties that originate from artificial sub wavelength structures although the lorentz metamaterial model has been used by physicists and electrical engineers its mathematical properties have not been investigated yet also more robust and efficient algorithms for time domain simulations are needed in this paper we initiate our work in this respect by developing some finite element schemes for solving the lorentz model stability and error analysis are proved for these schemes and 2 d numerical results justifying our theoretical results are presented

numerical analysis of a pml model for time dependent maxwell s equations in this paper we study a perfectly matched layer model for the three dimensional time dependent maxwell s equations we develop both semi and fully discrete finite element methods for solving the truncated pml problem by nedelec edge elements optimal convergence rates are proved for both semi and fully discrete schemes to our knowledge this is the first error analysis obtained for time domain finite element method for pml models

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

topological conjugacy of piecewise monotonic functions of nonmonotonicity height 1 abstract the conjugacy problem is an important topic in the theory of dynamical systems and functional equations in this paper we investigate a class of piecewise monotone and continuous maps with nonmonotonicity height 1 we give a sufficient and necessary condition under which any two of these maps are topologically conjugate and construct a topological conjugacy with an extension method if such a conjugacy exists

iterative roots of piecewise monotonic functions of nonmonotonicity height not less than 2 abstract it is known that any piecewise monotonic function of nonmonotonicity height not less than 2 has no continuous iterative roots of order greater than the number of forts of the function so the following problem arises naturally does such a function have an iterative root of order n not greater than the number of forts we consider the case that the number of forts is equal to n in which there appear possibly only two types t 1 and t 2 of iterative roots i e the roots strictly increasing on the interval stretched on all forts of the given function and the roots strictly decreasing on such an interval respectively we characterize all type t 1 roots of order n and give a necessary condition for a root of order n to be of type t 2 a full description of type t 2 is still an open question

a priori and posteriori error analysis for time dependent maxwell s equations abstract we consider time dependent maxwell s equations discretized by variable time steps in time domain and edge elements in spatial domain first the stability and optimal a priori error estimate are proved for both semi and fully discrete schemes then a posteriori error analysis is carried out for both schemes

a posteriori error estimates for nonconforming finite element methods computable a posteriori error bounds for a large class of nonconforming finite element methods are provided for a model poisson problem in two and three space dimensions besides a refined residual based a posteriori error estimate an averaging estimator is established and an l 2 estimate is included the a posteriori error estimates are reliable and efficient the proof of reliability relies on a helmholtz decomposition

global weak solutions for a two component camassa holm shallow water system abstract in this paper we prove the existence of global weak solution for an integrable two component camassa holm shallow water system provided the initial data satisfying some certain conditions

superconvergence analysis for maxwell s equations in dispersive media in this paper we consider the time dependent maxwell s equations in dispersive media on a bounded three dimensional domain global superconvergence is obtained for semi discrete mixed finite element methods for three most popular dispersive media models the isotropic cold plasma the one pole debye medium and the two pole lorentz medium global superconvergence for a standard finite element method is also presented to our best knowledge this is the first superconvergence analysis obtained for maxwell s equations when dispersive media are involved

wave breaking analysis for the periodic rotation two component camassa holm system abstract in this paper we study the blow up phenomenon of the initial boundary value problem for the periodic rotation two component camassa holm r2ch system the results include a precise blow up criterion when 0 and two new blow up statements and the exact blow up rate for strong solutions of the system

a priori and computable a posteriori error estimates for an hdg method for the coercive maxwell equations abstract in this paper we present and analyze a hybridizable discontinuous galerkin hdg method for a mixed curl curl formulation of the steady state coercive maxwell equations with a discrete sobolev embedding type estimates for the discontinuous polynomials we provide a priori error estimates for the electric field and the lagrange multiplier in the energy norm with the smooth or minimal regularity assumption on the exact solution we have optimal convergence rate for the electric field and the lagrange multiplier in the energy norm the a priori error estimate for the electric field in the l 2 norm is also obtained by the duality argument and the approximation is also optimal for the electric field in the l 2 norm moreover by employing suitable helmholtz decompositions of the error together with the upper bound estimate for the lagrange multiplier we provide a computable residual based a posteriori error estimator which is derived based on the error measured in terms of a mesh dependent energy norm the efficiency of the a posteriori error estimator is also established three dimensional numerical results testing the performance of the a priori and a posteriori error estimates for the maxwell equations are given

tri hamiltonian duality between solitons and solitary wave solutions having compact support a simple scaling argument shows that most integrable evolutionary systems which are known to admit a bi hamiltonian structure are in fact governed by a compatible trio of hamiltonian structures we demonstrate how their recombination leads to integrable hierarchies endowed with nonlinear dispersion that supports compactons solitary wave solutions having compact support or cusped and or peaked solitons a general algorithm for effecting this duality between classical solitons and their nonsmooth counterparts is illustrated by the construction of dual versions of the modified korteweg de vries equation the nonlinear schr odinger equation the integrable boussinesq system used to model the two way propagation of shallow water waves and the ito system of coupled nonlinear wave equations these hierarchies include a remarkable variety of interesting integrable nonlinear differential equations textcopyright 1996 the american physical society

computing iterative roots of polygonal functions based on the iterative root theory for monotone functions an algorithm for computing polygonal iterative roots of increasing polygonal functions was given by j kobza in this paper we not only give an algorithm for roots of decreasing polygonal functions but also generalize kobza s results to the general n furthermore we extend our algorithms for polygonal pm functions a class of non monotonic functions

a multiscale discontinuous galerkin method with the computational structure of a continuous galerkin method proliferation of degrees of freedom has plagued discontinuous galerkin methodology from its inception over 30 years ago this paper develops a new computational formulation that combines the advantages of discontinuous galerkin methods with the data structure of their continuous galerkin counterparts the new method uses local element wise problems to project a continuous finite element space into a given discontinuous space and then applies a discontinuous galerkin formulation the projection leads to parameterization of the discontinuous degrees of freedom by their continuous counterparts and has a variational multiscale interpretation this significantly reduces the computational burden and at the same time little or no degradation of the solution occurs in fact the new method produces improved solutions compared with the traditional discontinuous galerkin method in some situations

leading coefficient problem for polynomial like iterative equations abstract because of difficulties in applying fixed point theorems most of known results on the polynomial like iterative equation j 1 n j f j x f x were given by assuming 1 0 and the existence of solutions under the most natural assumption n 0 is an interesting problem called leading coefficient problem for this problem locally expansive invertible c 1 solutions are obtained in the expansive case and the non hyperbolic case in w zhang on existence for polynomial like iterative equations results math 45 2004 185 194 and c 0 increasing solutions are constructed in b xu w zhang construction of continuous solutions and stability for the polynomial like iterative equation j math anal appl 325 2007 1160 1170 in this paper we discuss c 1 solutions for more combinations between expansive mappings and contractive ones and combinations between increasing mappings and decreasing ones

topological conjugacy and transitivity for a class of piecewise monotone maps of the interval on dit qu une application continue f d un intervalle compact dans lui meme est markov lineaire s il est lineaire par morceaux et l ensemble de tous les f k x ou k 0 et x une extremite d un morceau lineaire est fini on donne une classification effective pour des applications de markov lineaires et une procedure effective pour determiner quand une telle application est transitive

koenigs embedding flow problem with global c1 smoothness which c1 orientation preserving diffeomorphisms on the compact interval 0 1 that of course fixing the end points can be embedded into a c1 flow on 0 1 is a difficult problem in the iteration theory such maps were proved to be rare in some references in this paper this problem is reduced to the relations between solutions of an ordinary differential equation and solutions of a functional equation by discussing those relations we describe a relatively wide class of orientation preserving diffeomorphisms on 0 1 which can achieve such a c1 flow our results are demonstrated by practical calculation for polygons

mixed discontinuous galerkin approximation of the maxwell operator we introduce and analyze a discontinuous galerkin discretization of the maxwell operator in mixed form here all the unknowns of the underlying system of partial differential equations are approximated by discontinuous finite element spaces of the same order for piecewise constant coefficients the method is shown to be stable and optimally convergent with respect to the mesh size numerical experiments highlighting the performance of the proposed method for problems with both smooth and singular analytical solutions are presented

linearization in two dimensions le choix des coordonnees linearisantes peut etre fait pour etre de classe c s ou s depend de la regularite r de la transformation et de la partie lineaire l on determine le supremum des valeurs s s l r comme exposant de holder quand l espace est a 2 dimensions et r un entier superieur a un on determine quand ce supremum est un maximum

transversal homoclinic points of a class of conservative diffeomorphisms abstract we develop a global graph transformation to obtain estimates for certain invariant manifolds of a class of area preserving diffeomorphisms with symmetries the existence of homoclinic or heteroclinic points and the analyticity of the angle between the invariant manifolds at them is proved for the henon and the standard maps a lower bound of this angle is given for a large set of values of the parameters

how violently do smooth iterative roots oscillate abstract a crisis in the smoothness of iterative roots appears at fixed points the local c r smoothness of iterative roots near a hyperbolic fixed point is well known but its global c r extension to both fixed points is generically impossible because of their violent oscillation near the next hyperbolic fixed point in this study we consider how violently these smooth iterative roots oscillate we prove that their first order derivatives are bounded but their r th r 2 order derivatives are generically unbounded in addition we prove that the global c 1 smoothness is of vital significance for the global higher order derivatives as a corollary we show that iterative roots on the maximal interval oscillate with c 1 boundedness but c r r 2 unboundedness

on fractional iterates of a brouwer homeomorphism embeddable in a flow we present a method for finding continuous and consequently homeomorphic orientation preserving iterative roots of a brouwer homeomorphism which is embeddable in a flow to obtain the roots we use a countable family of maximal parallelizable regions of the flow which is a cover of the plane the maximal parallelizable regions are unions of equivalence classes of an appropriate equivalence relation we show that if an equivalence class is invariant under the nth iterate of a brouwer homeomorphism g then it is invariant under g we use this fact to prove that each maximal parallelizable region of the flow must be invariant under all homeomorphic orientation preserving iterative roots of the given brouwer homeomorphism

blowup solutions for the generalized two component camassa holm system on the circle abstract in this paper we study the generalized two component camassa holm system which can be derived from the theory of shallow water waves moving over a linear shear flow we establish two sufficient conditions for wave breaking solutions with certain initial profiles

numerical convergence and physical fidelity analysis for maxwell s equations in metamaterials abstract in this paper we develop a leap frog mixed finite element method for solving maxwell s equations resulting from metamaterials our scheme is similar to the popular yee s fdtd scheme used in electrical engineering community and is preferable for three dimensional large scale modeling since no storage of the large coefficient matrix is needed our scheme is proved to obey the gauss s law automatically if the initial fields satisfy that furthermore the conditional stability and optimal error estimate for the proposed scheme are proved to our best knowledge we are unaware of any other publications devoted to the convergence analysis of this leap frog explicit scheme for maxwell s equations even in a simple medium while our results for metamaterials automatically reduce to the standard maxwell s equations in vacuum by dropping some terms resulting from the constitutive equations numerical results confirming our analysis are presented

the question on characteristic endpoints for iterative roots of pm functions abstract iterative roots of mappings are of special interests because it defines fractional iteration displays middle procedure of evolution and proposes a weak version of the embedding flow problem for pm functions of height 1 the class of 1 dimensional mappings having the simplest nonmonotonicity the existence of continuous iterative roots of any order was obtained under the characteristic endpoints condition and the condition was proved to be necessary for those orders greater than the number of forts plus 1 this suggests an open question about iterative roots without that condition called the question on characteristic endpoints in this paper the question is answered completely in the case that the number of forts is equal to the order although results of nonexistence are also obtained for the case that the number of forts is greater than the order a full description is still open

a finite volume method for the approximation of maxwell s equations in two space dimensions on arbitrary meshes a new finite volume method is presented for discretizing the two dimensional maxwell equations this method may be seen as an extension of the covolume type methods to arbitrary possibly non conforming or even non convex n sided polygonal meshes thanks to an appropriate choice of degrees of freedom an equivalent formulation of the scheme is given in terms of discrete differential operators obeying discrete duality principles the main properties of the scheme are its energy conservation its stability under a cfl like condition and the fact that it preserves gauss law and divergence free magnetic fields second order convergence is demonstrated numerically on non conforming and distorted meshes

efficient large scale electromagnetic simulations using dynamically adapted meshes with the discontinuous galerkin method a framework for performing dynamic mesh adaptation with the discontinuous galerkin method dgm is presented adaptations include modifications of the local mesh step size h adaptation and the local degree of the approximating polynomials p adaptation as well as their combination the computation of the approximation within locally adapted elements is based on projections between finite element spaces fes which are shown to preserve an upper limit of the electromagnetic energy the formulation supports high level hanging nodes and applies precomputation of surface integrals for increasing computational efficiency error and smoothness estimates based on interface jumps are presented and applied to the fully hp adaptive simulation of two examples in one dimensional space a full wave simulation of electromagnetic scattering from a radar reflector demonstrates the applicability to large scale problems in three dimensional space

non monotonic iterative roots extended from characteristic intervals it has been treated as a difficult problem to find iterative roots of non monotonic functions for some pm functions which do not increase the number of forts under iteration a method was given to obtain a non monotonic iterative root by extending a monotone iterative root from the characteristic interval in this paper we prove that every continuous iterative root is an extension from the characteristic interval and give various modes of extension for those iterative roots of pm functions

the general exact bijective continuous solution of feigenbaum s functional equation solutionsf of feigenbaum s functional equationf f x 1 f x where 0 is a fixed real number account for many of the fascinating properties of the behaviour of successive iterates of one parameter families of nonlinear maps in connection with the phenomenon of intermittency interesting families of exact solutions have recently been found for 0 these solutions can all be derived from continuous bijective solutions which are topologically equivalent to translations in this paper thegeneral exact continuous bijective solution is found for any 0 positive or negative in particular it is shown that forany 0 there are solutions which areinequivalent to translations and it is shown that bijective solutions equivalent to translations exist only when 0 1 these results considerably enlarge the stock of available exact solutions of feigenbaum s equation

construction of continuous solutions and stability for the polynomial like iterative equation abstract most of known results such as existence uniqueness and stability for polynomial like iterative equations were given under the assumption that the coefficient of the first order iteration term does not vanish the existence with a non zero leading coefficient was therefore raised as an open problem it was positively answered for local c 1 solutions later in this paper this problem is answered further by constructing c 0 solutions moreover we discuss the stability of those c 0 solutions which consequently implies a result of the stability for iterative roots

smooth linearization near a fixed point in this paper we extend a theorem of sternberg and bi leckii we study a vector field or a diffeomorphism in the vicinity of a hyperbolic fixed point we assume that the eigenvalues of the linear part a at the fixed point satisfy qth order algebraic inequalities where q 2 2 then there is ck linearization in the vicinity of the fixed point where k is the q smoothness of a we give an explicit and simple algorithm for com puting k an illustrative example from celestial mechanics is included which shows that our main theorem is an improvement over previously known theories we also show that if the vector field or diffeomorphism depends smoothly on a parameter then the linearizing conjugation de pends smoothly on the parameter

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

continuity of iteration and approximation of iterative roots motivated by computing iterative roots for general continuous functions in this paper we prove the continuity of the iteration operators t n defined by t nf f n we apply the continuity and introduce the concept of continuity degree to answer positively the approximation question if lim m f m f can we find an iterative root f m of f m of order n for each email protected n such that the sequence f m tends to the iterative root of f of order n associated with a given initial function we not only give the construction of such an approximating sequence f m but also illustrate the approximation of iterative roots with an example some remarks are presented in order to compare our approximation with the hyers ulam stability

convergence analysis of an adaptive interior penalty discontinuous galerkin method we study the convergence of an adaptive interior penalty discontinuous galerkin ipdg method for a two dimensional model second order elliptic boundary value problem based on a residual type a posteriori error estimator we prove that after each refinement step of the adaptive scheme we achieve a guaranteed reduction of the global discretization error in the mesh dependent energy norm associated with the ipdg method in contrast to recent work on adaptive ipdg methods o karakashian and f pascal convergence of adaptive discontinuous galerkin approximations of second order elliptic problems preprint university of tennessee knoxville tn 2007 the convergence analysis does not require multiple interior nodes for refined elements of the triangulation in fact it will be shown that bisection of the elements is sufficient the main ingredients of the proof of the error reduction property are the reliability and a perturbed discrete local efficiency of the estimator a bulk criterion that takes care of a proper selection of edges and elements for refinement and a perturbed galerkin orthogonality property with respect to the energy inner product the results of numerical experiments are given to illustrate the performance of the adaptive method

iterative roots of piecewise monotonic functions with finite nonmonotonicity height abstract it is known that any continuous piecewise monotonic function with nonmonotonicity height not less than 2 has no continuous iterative roots of order n greater than the number of forts of the function in this paper we consider the problem of iterative roots in the case that the order n is less than or equal to the number of forts by investigating the trajectory of possible continuous roots we give a general method to find all iterative roots of those functions with finite nonmonotonicity height

singular solutions of a modified two component camassa holm equation the camassa holm ch equation is a well known integrable equation describing the velocity dynamics of shallow water waves this equation exhibits spontaneous emergence of singular solutions peakons from smooth initial conditions the ch equation has been recently extended to a two component integrable system ch2 which includes both velocity and density variables in the dynamics although possessing peakon solutions in the velocity the ch2 equation does not admit singular solutions in the density profile we modify the ch2 system to allow a dependence on the average density as well as the pointwise density the modified ch2 system mch2 does admit peakon solutions in the velocity and average density we analytically identify the steepening mechanism that allows the singular solutions to emerge from smooth spatially confined initial data numerical results for the mch2 system are given and compared with the pure ch2 case these numerics show that the modification in the mch2 system to introduce the average density has little short time effect on the emergent dynamical properties however an analytical and numerical study of pairwise peakon interactions for the mch2 system shows a different asymptotic feature namely besides the expected soliton scattering behavior seen in overtaking and head on peakon collisions the mch2 system also allows the phase shift of the peakon collision to diverge in certain parameter regimes

a posteriori error estimator based on gradient recovery by averaging for discontinuous galerkin methods we consider some anisotropic and piecewise constant diffusion problems in domains of r 2 approximated by a discontinuous galerkin method with polynomials of any fixed degree we propose an a posteriori error estimator based on gradient recovery by averaging it is shown that this estimator gives rise to an upper bound where the constant is one up to some additional terms that guarantee reliability the lower bound is also established moreover these additional terms are negligible when the recovered gradient is superconvergent the reliability and efficiency of the proposed estimator is confirmed by some numerical tests

a discontinuoushpfinite element method for diffusion problems we present an extension of the discontinuous galerkin method which is applicable to the numerical solution of diffusion problems the method involves a weak imposition of continuity conditions on the solution values and on fluxes across interelement boundaries within each element arbitrary spectral approximations can be constructed with different orderspin each element we demonstrate that the method is elementwise conservative a property uncharacteristic of high order finite elements for clarity we focus on a model class of linear second order boundary value problems and we developpriorierror estimates convergence proofs and stability estimates the results of numerical experiments onh andp convergence rates for representative two dimensional problems suggest that the method is robust and capable of delivering exponential rates of convergence

a note on iterative roots of pm functions abstract in this paper we study iterative roots of pm functions a special class of non monotone functions problem 2 in w zhang pm functions their characteristic intervals and iterative roots ann polon math lxv 1997 119 128 is solved partly and theorem 4 in that paper is generalized

energy norm a posteriori error estimation for discontinuous galerkin methods in this paper we present a residual based a posteriori error estimate of a natural mesh dependent energy norm of the error in a family of discontinuous galerkin approximations of elliptic problems the theory is developed for an elliptic model problem in two and three spatial dimensions and general nonconvex polygonal domains are allowed we also present some illustrating numerical examples

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

a discontinuous galerkin surface integral equation method for electromagnetic wave scattering from nonpenetrable targets we present a discontinuous galerkin surface integral equation method herein referred to as iedg for time harmonic electromagnetic wave scattering from nonpenetrable targets the proposed iedg algorithm allows the implementation of the combined field integral equation cfie using square integrable trial and test functions without any considerations of continuity requirements across element boundaries due to the local characteristics of basis functions it is possible to employ nonconformal surface discretizations of the targets furthermore it enables the possibility to mix different types of elements and employ different order of basis functions within the same discretization therefore the proposed iedg method is highly flexible to apply adaptation techniques numerical results are included to validate the accuracy and demonstrate the versatility of the proposed iedg method in addition a complex large scale simulation is conducted to illustrate the potential benefits offered by the proposed method for modeling multiscale electrically large targets

exact steady periodic water waves with vorticity we consider the classical water wave problem described by the euler equations with a free surface under the influence of gravity over a flat bottom we construct two dimensional inviscid periodic traveling waves with vorticity they are symmetric waves whose profiles are monotone between each crest and trough we use bifurcation and degree theory to construct a global connected set of such solutions c 2004 wiley periodicals inc

global existence and blow up phenomena for an integrable two component camassa holm shallow water system abstract this paper is concerned with global existence and blow up phenomena for an integrable two component camassa holm shallow water system a new global existence result and several new blow up results of strong solutions to the system are presented our obtained results for the system are sharp and improve considerably earlier results

locking free adaptive discontinuous galerkin fem for linear elasticity problems an adaptive discontinuous galerkin finite element method for linear elasticity problems is presented we develop an a posteriori error estimate and prove its robustness with respect to nearly incompressible materials absence of volume locking furthermore we present some numerical experiments which illustrate the performance of the scheme on adaptively refined meshes

energy norm a posteriori error estimation for mixed discontinuous galerkin approximations of the maxwell operator in this paper we develop the a posteriori error estimation of mixed discontinuous galerkin finite element approximations of the maxwell operator in particular by employing suitable helmholtz decompositions of the error together with the conservation properties of the underlying method computable upper bounds on the error measured in terms of a natural mesh dependent energy norm are derived numerical experiments testing the performance of our a posteriori error bounds for problems with both smooth and singular analytical solutions are presented

iterative functional equation x x t f t with f t piecewise linear the equation x x t f t is discussed in many papers purely from the theoretical point of view existence properties we consider the properties of the solution and corresponding algorithms for computing the exact solution of such equations in the case of f t being a line or polygon

well posedness and blow up solution for a modified two component periodic camassa holm system with peakons considered herein is a modified two component periodic camassa holm system with peakons the local well posedness and low regularity result of solutions are established the precise blow up scenarios of strong solutions and several results of blow up solutions with certain initial profiles are described in detail and the exact blow up rate is also obtained