a two dimensional eshelby problem for two bonded piezoelectric half planes the present paper concerns a two dimensional eshelby problem for an inclusion of arbitrary shape embedded within one of two bonded dissimilar piezoelectric halfplanes the elastic and piezoelectric constants of the inclusion and its surrounding half plane are assumed to be the same a simple explicit solution is derived in terms of some auxiliary functions which can be determined using several related conformal mappings of the inclusion shape the obtained solution is exact provided that the expansions of all conformal mappings include only a finite number of terms on the other hand if an exact conformal mapping includes infinite terms a truncated polynomial mapping function should be used and then the method gives an approximate solution the existing solutions obtained in an earlier work for a homogeneous piezoelectric plane or half plane can be derived from the present solution as special cases in particular the closed form solutions are given for the eshelby problem of an arbitrarily shaped inclusion in a piezoelectric half plane with various mixed surface conditions such as rigid insulating surface or traction free conducting surface these solutions are used to study the effects of various surface electrical conditions on an electro elastic field in a piezoelectric half plane

existence and mann iterative approximations of nonoscillatory solutions of nth order neutral delay differential equations abstract in this paper we consider the following nth order neutral delay differential equation d n d t n x t c x t 1 n 1 f t x t 1 x t 2 x t k g t t t 0 where n is a positive integer c r 0 i 0 for i 1 k f c t 0 r k r and g c t 0 r by employing the contraction mapping principle we obtain several existence results of nonoscillatory solutions for the above equation construct a few mann type iterative approximation schemes for these nonoscillatory solutions and establish several error estimates between the approximate solutions and the nonoscillatory solutions in addition we obtain some sufficient conditions for the existence of infinitely many nonoscillatory solutions these results presented in this paper extend improve and unify many known results due to cheng and annie j f cheng z annie existence of nonoscillatory solution to second order linear neutral delay equation j systems sci math sci 24 2004 389 397 in chinese graef yang and zhang j r graef b yang b g zhang existence of nonoscillatory and oscillatory solutions of neutral differential equations with positive and negative coefficients math bohem 124 1999 87 102 kulenovic and had iomerspahic m r s kulenovic s had iomerspahic existence of nonoscillatory solution of second order linear neutral delay equation j math anal appl 228 1998 436 448 m r s kulenovic s had iomerspahic existence of nonoscillatory solution for linear neutral delay equation fasc math 32 2001 61 72 zhang and yu b g zhang j s yu on the existence of asymptotically decaying positive solutions of second order neutral differential equations j math anal appl 166 1992 1 11 zhang b g zhang on the positive solutions of a kind of neutral equations acta math appl sinica 19 1996 222 230 and zhou and zhang y zhou b g zhang existence of nonoscillatory solutions of higher order neutral differential equations with positive and negative coefficients appl math lett 15 2002 867 874 and others some nontrivial examples are given to illustrate the advantages of our results

green s functions of two dimensional anisotropic plates containing an elliptic hole abstract for a two dimensional anisotropic plate the green s function satisfying traction free boundary conditions around an elliptic hole is developed using stroh s formalism a combination of this function and the boundary element method shows that it is the most effective approach for solving hole problems the generality of the present green s function is shown by the broader meaning of the following words two dimensional includes not only in plane but also antiplane problems and the problems where in plane and anti plane deformations couple each other anisotropic which need not have any material symmetry restrictions means that it covers the solutions given in the literature which only deal with orthotropic or monoclinic materials elliptic includes the special case where the minor axis of the ellipse tends to zero i e the case of a griffith crack the accuracy of the numerical method presented is then verified by comparison with exact or accepted solutions of several examples such as an infinite or a finite plate with an elliptic hole or a crack under in plane or anti plane loading the materials used are isotropic orthotropic or laminated composites finally problems where the hole boundary is not traction free are solved such as rigid inclusions and pin loaded holes

on local solutions of the initial value problem for the vlasov maxwell equation the initial value problem of the vlasov maxwell equation has a unique solution in a time interval 0 t for each initial data in some function space t is estimated by the size of the initial data the solution is classical if the initial data is smooth

propagation of moments and regularity for the 3 dimensional vlasov poisson system we prove that if the initial data has moments inv higher than three then the solution of vlasov poisson has also moments inv higher than three we deduce from this different regularity results on the local density the force field or the solution itself also we give a new uniqueness result and new regularity results for solutions satisfying only the energy andl bounds our proofs are based on a new representation formula and logarithmic estimates for the force field

a further investigation of green s functions for a piezoelectric material with a cavity or a crack abstract in this paper the green s functions of an infinite two dimensional piezoelectric material containing an elliptical cavity are re investigated by introducing exact electric boundary conditions on the hole boundary and the corresponding modified solutions are obtained by setting 0 the dielectric constant in the cavity to be zero the modified green s functions are returned to the conventional ones lu and williams 1998 furthermore the hoop stresses along the hole boundary under the action of a set of generalized concentrated forces are obtained when the hole is reduced to a slit crack the expressions of generalized stress intensity factors are also provided

infinite sequence of parallel cracks in an anisotropic piezoelectric solid in this paper the problem of an infinite sequence of parallel cracks in an infinite extended piezoelectric solid is analyzed a system of singular integral equations is formulated for general anisotropic piezoelectric materials of which the kernel functions developed are in complex form for commonly used transversely isotropic piezoelectric materials the kernel functions are given in real forms furthermore the obtained real kernel functions may be reduced respectively to those kernel functions for purely elastic and purely electric problems when the coupled mechanical and electric effects disappear the system of singular integral equations is solved numerically and the coupling effects of the mechanical and electric phenomena are presented by the generalized stress intensity factors

higher regularity of the tangential fields in the relativistic vlasov maxwell system abstract it is shown that the tangential electric and magnetic fields in the glassey strauss representation formulas are in fact bounded in l loc t l x 2 for some 0

dynamic green s functions in anisotropic piezoelectric thermoelastic and poroelastic solids a procedure is described to generate fundamental solutions or green s functions for time harmonic point forces and sources the linearity of the field equations permits the green s function to be represented as an integral over the surface of a unit sphere where the integrand is the solution of a one dimensional impulse response problem the method is demonstrated for the theories of piezoelectricity thermoelasticity and poroelasticity time domain analogues are discussed and compared with known expressions for anisotropic elasticity

classical solutions and the glassey strauss theorem for the 3d vlasov maxwell system r glassey and w strauss have proved in arch rational mech anal 92 1986 59 90 that c1 solutions to the relativistic vlasov maxwell system in three space dimensions do not develop singularities as long as the support of the distribution function in the momentum variable remains bounded the present paper simplifies their proof

a new continuation criterion for the relativistic vlasov maxwell system the global existence of solutions to the relativistic vlasov maxwell system given sufficiently regular finite energy initial data is a longstanding open problem the main result of glassey and strauss arch ration mech anal 92 59 90 1986 shows that a solution f e b remains c 1 as long as the momentum support of f remains bounded alternate proofs were later given by bouchut et al arch ration mech anal 170 1 15 2003 and klainerman and staffilani commun pure appl anal 1 103 125 2002 we show that only the boundedness of the momentum support of f after projecting to any two dimensional plane is needed for f e b to remain c 1

endpoint strichartz estimates we prove an abstract strichartz estimate which implies previously unknown endpoint strichartz estimates for the wave equation in dimension n 4 and the schrodinger equation in dimension n 3 three other applications are discussed local existence for a nonlinear wave equation and strichartz type estimates for more general dispersive equations and for the kinetic transport equation

stability of periodic steady state solutions to a non isentropic euler poisson system abstract we study the stability of periodic smooth solutions near non constant steady states for a non isentropic euler poisson system without temperature damping term the system arises in the theory of semiconductors for which the doping profile is a given smooth function in this stability problem there are no special restrictions on the size of the doping profile but only on the size of the perturbation we prove that small perturbations of periodic steady states are exponentially stable for large time for this purpose we introduce new variables and choose a non diagonal symmetrizer of the full euler equations to recover dissipation estimates this also allows to make the proof of the stability result very simple and concise

existence for nonoscillatory solutions of second order nonlinear differential equations abstract in this paper the existence of nonoscillatory solutions of the second order nonlinear neutral differential equation r t x t p t x t i 1 m q i t f i x t i 0 t t 0 where m 1 is an integer 0 i 0 r p q i c t 0 r f i c r r i 1 2 m are studied some new sufficient conditions for the existence of a nonoscillatory solution of above equation are obtained for general p t and q i t i 1 2 m which means that we allow oscillatory p t and q i t i 1 2 m in particular our results improve essentially and extend some known results in the recent references

existence and iterative approximations of nonoscillatory solutions of higher order nonlinear neutral delay differential equations this paper studies a few existence results of nonoscillatory solutions for the following higher order nonlinear neutral delay differential equation dndtnx t cx t 1 n i 1didtih t x h1 t x h2 t x hk t 1 n 1f t x f1 t x f2 t x fk t g t t t0 where n is a positive integer 0 i n 1 c r 1 0 h ci t0 rk r f c t0 rk r g c t0 r hl ci t0 r and fl c t0 r with limt hl t limt fl t l 1 k constructs several mann type iterative approximation sequences with errors for these nonoscillatory solutions and establish some error estimates between the approximate solutions and the nonoscillatory solutions in addition sufficient conditions for the existence of infinitely many nonoscillatory solutions for the above equation are given three nontrivial examples are given to illustrate the advantages of our results

a boundary integral formulation and 2d fundamental solutions for piezoelectric media abstract first based on the basic equations of piezoelectricity the boundary integral formulation is derived by utilizing the reciprocal work theorem second for the plane problem of piezoelectric media one general solution in terms of harmonic functions is derived and the fundamental solutions are therefore obtained numerical calculations by boundary element method bem are performed to give the stress concentration coefficient of an infinite piezoelectric plane with a circular hole as well as the stress and electric intensity factors of a central crack locating on an infinite plate results are found to agree well with the exact solutions

general solution for eshelby s problem of 2d arbitrarily shaped piezoelectric inclusions abstract eshelby s problem of piezoelectric inclusions arises sometimes in exploiting the electromechanical coupling effect in piezoelectric media for example it intervenes in the nanostructure design of strained semiconductor devices involving strain induced quantum dot qd and quantum wire qwr growth using the extended stroh formalism the present work gives a general analytical solution for eshelby s problem of two dimensional arbitrarily shaped piezoelectric inclusions the key step toward obtaining this general solution is the derivation of a simple and compact boundary integral expression for the eigenfunctions in the extended stroh formalism applied to eshelby s problem the simplicity and compactness of the boundary integral expression derived make it much less difficult to analytically tackle eshelby s piezoelectric problem for a large variety of non elliptical inclusions in the present work explicit analytical solutions are obtained and detailed for all polygonal inclusions and for the inclusions characterized by jordan s curves and laurent s polynomials by considering the piezoelectric material gaas 110 the analytical solutions provided are illustrated numerically to verify the coincidence between different expressions and to clarify the jump across the boundary of the inclusion and the singularity around the corner of the inclusion

existence of nonoscillatory solution of second order linear neutral delay equation consider the neutral delay differential equation with positive and negative coefficients formula wherep rand formula some sufficient conditions for the existence of a nonoscillatory solution of the above equation expressed in terms of sqi s ds i 1 2 and certain technical conditions implying thatq1 s dominatesq2 s are obtained for values ofp 1

permanent regimes for the vlasov maxwell equations with specular boundary conditions the subject matter of this paper concerns the existence of permanent regimes i e stationary or time periodic solutions for the vlasov maxwell system in a bounded domain we are looking for equilibrium configurations by imposing specular boundary conditions the main difficulty is the treatment of such boundary conditions our analysis relies on perturbative techniques based on uniform a priori estimates

strichartz estimates and moment bounds for the relativistic vlasov maxwell system we consider the relativistic vlasov maxwell system with data of unrestricted size and without compact support in momentum space in the two dimensional and the two and a half dimensional cases glassey schaeffer proved commun math phys 185 257 284 1997 arch ration mech anal 141 331 354 1998 arch ration mech anal 141 355 374 1998 that for regular initial data with compact momentum support this system has unique global in time classical solutions in this work we do not assume compact momentum support for the initial data and instead require only that the data have polynomial decay in momentum space in the two dimensional and the two and a half dimensional cases we prove the global existence uniqueness and regularity for solutions arising from this class of initial data to this end we use strichartz estimates and prove that suitable moments of the solution remain bounded moreover we obtain a slight improvement of the temporal growth of the l infty x norms of the electromagnetic fields compared to glassey and schaeffer commun math phys 185 257 284 1997 arch ration mech anal 141 355 374 1998 in the three dimensional case we apply strichartz estimates and moment bounds to show that a regular solution can be extended as long as p 0 theta f l q x l 1 p remains bounded for theta frac 2 q 2 q leqq infty this improves previous results of pallard indiana univ math j 54 5 1395 1409 2005 commun math sci 13 2 347 354 2015

asymptotic behavior of weak solutions for the relativistic vlasov maxwell equations with large light speed abstract we study here the behavior of time periodic weak solutions for the relativistic vlasov maxwell boundary value problem in a three dimensional bounded domain with strictly star shaped boundary when the light speed becomes infinite we prove the convergence toward a time periodic weak solution for the classical vlasov poisson equations

non oscillatory solutions for a nonlinear neutral delay differential equation abstract we study the existence of non oscillatory bounded solutions for a second order nonlinear neutral delay differential equation some sufficient conditions for the existence of non oscillatory bounded solutions with positive lower bound or negative upper bound are established and the non oscillatory solutions with decay as t are discussed

solvability and iterative algorithms for a higher order nonlinear neutral delay differential equation the paper is concerned with the higher order nonlinear neutral delay differential equation r t x t p t x email protected m n m 1 n m 1ft email protected 1 t x s l t g t t t 0 using the banach fixed point theorem we establish five existence results of uncountably many bounded nonoscillatory solutions for the above equation construct five mann iterative sequences with mixed errors for approximating these nonoscillatory solutions and discuss five error estimates between the approximate solutions and these nonoscillatory solutions to dwell the importance and applications of our results five nontrivial examples are constructed

three new results on continuation criteria for the 3d relativistic vlasov maxwell system abstract we consider continuation criteria for the three dimensional relativistic vlasov maxwell system when the particle density f t x p is compactly supported at t 0 we prove p 0 18 5 r 1 f l t l x r l p 1 1 where 1 r 2 and 0 is arbitrarily small is a continuation criteria our continuation criteria is an improvement in the 1 r 2 range to the previously best known criteria p 0 4 r 1 f l t l x r l 1 p 1 due to kunze 7 we also consider continuation criteria when f 0 x p has noncompact support in this regime luk strain 9 proved that p 0 f l x 1 l p 1 1 is a continuation criteria for 5 we improve this result to 3 finally we build on another result by luk strain 8 the authors proved boundedness of momentum support on a fixed two dimensional plane is a sufficient continuation criteria we prove the same result even if the plane varies continuously in time

nonoscillatory solutions for system of neutral delay equation abstract consider the system of neutral delay differential equations d d t x t p x t q t x t 0 where p r 0 0 and q is continuous matrix and the system d d t x t b x t q t x t 0 where b is a matrix we obtain the sufficient condition for the existence of certain types of solutions of the above equation to be q s d s for p 1

finite speed propagation of the solutions for the relativistic vlasov maxwell system in this paper we investigate the continuous dependence with respect to the initial data of the solutions for the 1d and 1 5d relativistic vlasov maxwell system more precisely we prove that these solutions propagate with finite speed we formulate our results in the framework of mild solutions i e the particle densities are solutions by characteristics and the electro magnetic fields are lipschitz continuous functions

dynamic representation formulas and fundamental solutions for piezoelectricity abstract representation formulas and fundamental solutions of the governing equations of transient piezoelectricity are obtained through a generalization of the reciprocal theorem and the plane wave transform method it is shown that dynamic fundamental and singular solutions can be reduced to one dimensional integral expressions by means of a slowness surface the article provides the necessary mathematical foundations towards the development of the boundary element method for nonstationary three dimensional electroelastic problems

infinitely many nonoscillatory solutions for second order nonlinear neutral delay differential equations abstract in this paper we consider the second order nonlinear neutral delay differential equation a t x t b t x t h t x h 1 t x h 2 t x h k t f t x f 1 t x f 2 t x f k t g t t t 0 where 0 a b g c t 0 r with a t 0 for t t 0 h c 1 t 0 r k r f c t 0 r k r h l c 1 t 0 r and f l c t 0 r with lim t h l t lim t f l t l 1 k under suitable conditions by making use of the banach fixed point theorem we show the existence of infinitely many nonoscillatory solutions which are uncountable for the above equation suggest several mann type iterative approximation sequences with errors for these nonoscillatory solutions and establish some error estimates between the approximate solutions and the nonoscillatory solutions five nontrivial examples are given to illustrate the advantages of our results

global classical solutions to the 3d nordstrom vlasov system the nordstrom vlasov system describes the kinetic evolution of self gravitating collisionless matter in the framework of a relativistic scalar theory of gravitation we prove global existence and uniqueness of classical solutions for the corresponding initial value problem in three dimensions when the initial data for the scalar field are smooth and the initial particle density is smooth with compact support

yet another criterion for global existence in the 3d relativistic vlasov maxwell system abstract we prove that solutions of the 3d relativistic vlasov maxwell system can be extended as long as the quantity 1 t x max 1 r 3 d p 1 p 2 1 1 v f t x p is bounded in l x 2

eshelby s problem for two dimensional piezoelectric inclusions of arbitrary shape eshelby s problem for piezoelectric inclusions of arbitrarily shaped crosssection remains a challenging topic in this paper a simple method is presented to obtain an analytic solution for eshelby

green functions of piezoelectric material with an elliptic hole or inclusion abstract in this paper the green functions of infinite two dimensional piezoelectric material containing an elliptic hole or an elliptic piezoelectric inclusion are obtained with the extended stroh formalism the results can be used to investigate the mechanical electric coupling behaviours of infinite piezoelectric material with hole or inclusion acted by a set of generalized concentrated forces and more importantly as kernels of boundary integral equations in bem analyses for finite size piezoelectric materials with general forces and boundary conditions