growth and decay of shock and acceleration waves in a traffic flow model with relaxation abstract the usual ficken based constitutive relation for traffic flux is replaced with one based on the maxwell cattaneo model the resulting flux law which now takes into account the reaction time of driver and vehicle results in a second order hyperbolic generalization of burgers equation as the pde governing the traffic density an analytical study of this equation is presented with an emphasis on shock and related kinematic wave phenomena specifically the exact traveling wave solution tws is derived and it is shown that shock formation is possible only if the diffusivity is non vanishing using singular surface theory exact amplitude expressions for both shock and acceleration waves are obtained and their temporal evolution determined the exact upper bound of the reaction time parameter is established and connections between singular surface and tws results are noted

homoclinic tangencies and hyperbolicity for surface diffeomorphisms we prove here that in the complement of the closure of the hyperbolic surface diffeomorphisms the ones exhibiting a homoclinic tangency are c 1 dense this represents a step towards the global understanding of dynamics of surface diffeomorphisms

a comparison of regularizations for an ill posed problem we consider numerical methods for a quasi boundary value regularization of the backward parabolic problem given by u t au 0 0 t t u t f where a is positive self adjoint and unbounded the regularization due to clark and oppenheimer perturbs the final value u t by adding u 0 where is a small parameter we show how this leads very naturally to a reformulation of the problem as a second kind fredholm integral equation which can be very easily approximated using methods previously developed by ames and epperson error estimates and examples are provided we also compare the regularization used here with that from ames and epperson

some links between recent gradient thermo elasto plasticity theories and the thermomechanics of generalized continua this work elaborates upon two robust models of gradient elasticity and gradient plasticity and one gradient model of heat transfer as originally advocated by the second author in the 1980 s the objective is after recalling the links between these models and existing generalized continuum theories as developed in the 1960 s and subsequently to apply the same methodology to the case of diffusion with a view to establishing generalized transport equations aifantis double diffusivity and conductivity theory that provides generalized mass or heat transfer equations is compared to micromorphic type hyper temperature and micro entropy proposals the double temperature and the micromorphic thermal models are shown to lead to equations more general that cattaneo s the sign of the coefficient of the second time derivative of temperature is found to differ according to both approaches the double temperature model contains a fourth space derivative term not present in the micromorphic models such generalized equations can be useful for example in the interpretation of recent femtosecond laser experiments on metals

continuous dependence on initial time geometry for a thermoelastic system with sign indefinite elasticities abstract continuous dependence of the solution to the equations of dynamical linear thermoelasticity on the initial time geometry is investigated using a lagrange identity method and assuming only the major symmetry on the elasticities but no sign definiteness we derive inequalities establishing that appropriately constrained solutions depend holder continuously on perturbations of the initial geometry

exponential stability to localized type iii thermoelasticity abstract this paper investigates the system proposed by a wave equation and a heat equation of type iii in one part of the domain a wave equation and a heat equation of type ii in another part of the domain coupled in a certain pattern in this paper we prove the exponential stability of the solutions under suitable conditions for the thermal conductivity and coupling term

parameter dependence of solutions of differential equations on spaces of distributions and the splitting of short exact sequences we show that a linear partial differential operator with constant coefficients p d is surjective on the space of e valued ultra distributions over an arbitrary convex set if e is a nuclear frechet space with property dn in particular this holds if e is isomorphic to the space of tempered distributions s or to the space of germs of holomorphic functions over a one point set h 0 this result has an interpretation in terms of solving the scalar equation p d u f such that the solution u depends on parameter whenever the right hand side f also depends on the parameter in the same way a suitable analogue for surjective convolution operators over rd is obtained as well to get the above results we develop a splitting theory for short exact sequences of the form 0 x y z 0 where z is a frechet schwartz space and x y are pls spaces like the spaces of distributions or real analytic functions or their subspaces in particular an extension of the dn splitting theorem of vogt and wagner is obtained

on the exponential decay in thermoelasticity without energy dissipation and of type iii in presence of an absorbing boundary we study the asymptotic behavior of the solution of a 3d hyperbolic system arising in the green naghdi models of thermoelasticity of type ii and iii with a dissipative boundary condition for the displacement and prove that the energy exponentially decays in time

a porous thermoelastic problem in this paper a porous thermoelastic problem is numerically considered the variational formulation is written as a coupled system of two hyperbolic equations for the displacement and the porosity fields and a parabolic equation for the temperature field an existence and uniqueness result as well as an energy decay property are recalled then fully discrete approximations are introduced by using the finite element method to approximate the spatial variable and the backward euler scheme to discretize the first order time derivatives a priori error estimates are proved from which the linear convergence is deduced under some additional regularity conditions finally some one and two dimensional numerical simulations are presented to show the accuracy of the approximation and the behavior of the solution

on countably strong fuzzy compact sets in l fuzzy topological spaces abstract in this paper the concept of countably strong fuzzy compact subsets in l fuzzy topological spaces has been presented by taking strong fuzzy compactness which is due to lowen 1978 as background the basic properties of countably strong fuzzy compact subsets have been discussed some characterizations of countably strong fuzzy compact subsets have been given by taking the stratum structures of l fuzzy sets as the point of departure also it is pointed out that countably strong fuzzy compactness is an l good extension of usual countably compactness

global hyperbolicity of renormalization for c r unimodal mappings in this paper we extend m lyubichi s recent results on the global hyperbolicity of renormalization of quadratic like germs to the space of cr unimodal maps with quadratic critical point we show that in this space the boundedtype limit sets of the renormalization operator have an invariant hyperbolic structure provided r i 2 a with a close to one as an intermediate step between lyubichi s results and ours we prove that the renormalization operator is hyperbolic in a banach space of real analytic maps we construct the local stable manifolds and prove that they form a continuous lamination whose leaves are c1 codimension one banach submanifolds of the ambient space and whose holonomy is c1 for some 0 we also prove that the global stable sets are c1 immersed codimension one submanifolds as well provided r i 3 a with a close to one as a corollary we deduce that in generic oneparameter families of cr unimodal maps the set of parameters corresponding to infinitely renormalizable maps of bounded combinatorial type is a cantor set with hausdorff dimension less than one

a new fuzzy compactness defined by fuzzy nets compactness is one of the most important notions in topology and is thoroughly investigated in general topology but it seems that the research about this notion in the area of fuzzy topology is not so effective as in general topology in fact it would seem that there was not even a good definition of compactness in this area until recently indeed soon after the famous article written by zadeh 8 was published chang 1 introduced the notion of fuzzy topological spaces and at the same time a certain fuzzy compactness was given from then on a series of different notions of fuzzy compactness have been discussed 2 3 71 and in 5 they were compared in detail but it seems unsatisfactory that all these fuzzy compactness ideas are defined for the whole fuzzy topological space but not for an arbitrary fuzzy subset therefore they are far from the crisp compactness for example it is impossible to discuss the hereditary property with respect to closed subsets of fuzzy compactness in 1977 pu and liu introduced the notion of fuzzy nets and a new concept of so called q neighborhood was given which could reflect the features of neighborhood structure in fuzzy topological spaces and by this new neighborhood structure the moore smith convergence theory was established spendidly 6 it furnishes us a basic tool to investigate the fuzzy compactness in a more general way to investigate the compactness of arbitrary fuzzy subsets in this paper a new fuzzy compactness defined by fuzzy nets we shall call it n compactness is given but we introduce the notion of r neighborhood see section 2 instead of qneighborhood to establish the moore smith convergence theory for it is perhaps more convennient to use n compactness possesses the following properties 1 n compactness is defined for arbitrary fuzzy subsets 2 for n compactness the hereditary property with respect to closed subsets holds 3 n compactness is a good extension 5 4 the continuous images of ncompact sets are n compact 5 for n compactness the tychonoff product theorem holds 6 if an n compact fuzzy topological space is t2 6 then it will satisfy a stronger separation axiom which will be called t4 in this paper 1 0022 247x 83 3 00

a unified procedure for construction of theories of deformable media i classical continuum physics a new unified procedure for constructing continuum theories of deformable media is presented and used in this and a companion paper the procedure starts with a balance of energy and derives from it all the relevant balance laws that may also include those that are associated with thermal electrical and magnetic effects the basic energetic ingredients that are included in the balance of energy depend of course on the nature of the particular theory of material behaviour desired the advantage of the new procedure becomes especially apparent when one considers formulation of a new theory of material behaviour for which additional balance laws involving new kinetic quantities are required to accompany any additional basic kinematic and thermal variables additional to those in the classical formulation indeed in the formulation of such new theories usually little or no previous information is available concerning properties of the new kinetic quantities in the additional balance laws and in this connection the unified procedure of this paper provides a simple attractive setting for deriving the basic equations that are automatically consistent with the energy balance in this paper first the basic features of the new procedure are illustrated in the context of classical thermomechanics generalizations of this thermomechanical theory are then discussed in two cases 1 in the presence of an additional kinematic variable and 2 in the presence of full electromagnetic effects both of these generalizations bring out some interesting novel features when new theories are being constructed

lowen s compactness in l fuzzy topological spaces abstract r lowen has introducedin 1976 a fuzzy compactness for fuzzy topological spaces wang has generalized it in 1988 to l fuzzy topological spaces and given it a characterization by means of nets in this paper we obtain some new characterization for lowen s compactness in l fuzzy topological spaces means of remote neighborhood families r covers filters and the family of closed l fuzzy subsets which has the finite intersection property in addition we have proved that lowen s compactness is an l good extension of usual compactness in general topological spaces

variational integrators for the dynamics of thermo elastic solids with finite speed thermal waves this paper formulates variational integrators for finite element discretizations of deformable bodies with heat conduction in the form of finite speed thermal waves the cornerstone of the construction consists in taking advantage of the fact that the green naghdi theory of type ii for thermo elastic solids has a hamiltonian structure thus standard techniques to construct variational integrators can be applied to finite element discretizations of the problem the resulting discrete in time trajectories are then consistent with the laws of thermodynamics for these systems for an isolated system they exactly conserve the total entropy and nearly exactly conserve the total energy over exponentially long periods of time moreover linear and angular momenta are also exactly conserved whenever the exact system does for definiteness we construct an explicit second order accurate algorithm for affine tetrahedral elements in two and three dimensions and demonstrate its performance with numerical examples

the dynamics of the henon map the purpose of this paper is to develop machinery which is suitable for a study of the long time behavior of systems such as the henon map with expansion combined with strong contraction our study is modeled on the treatment of the one dimensional system x 1 ax 2 and we study the perturbation of a from the value a 2 and b small a surprising number of complications arise when b 0 the computer simulations give some indication of the complicated structure of the attractor but it can safely be stated that the real difficulties do not show up the central aim of the paper is to introduce what we consider the relevant concepts and techniques needed to study mappings such as the henon one

chirality in isotropic linear gradient elasticity abstract chirality is generally speaking the property of an object that can be classified as left or right handed though it plays an important role in many branches of science chirality is encountered less often in continuum mechanics so most classical material models do not account for it in the context of elasticity for example classical elasticity is not chiral leading different authors to use cosserat elasticity to allow modelling of chiral behaviour gradient elasticity can also model chiral behaviour however this has received much less attention than its cosserat counterpart this paper shows how in the case of isotropic linear gradient elasticity a single additional parameter can be introduced that describes chiral behaviour this additional parameter directly linked to three dimensional deformation can be either negative or positive with its sign indicating a discrimination between the two opposite directions of torsion two simple examples are presented to show the practical effects of the chiral behaviour

growth and uniqueness in thermoelasticity a uniqueness theorem is proved for two theories of thermoelasticity capable of admitting finite speed thermal waves the theories having been proposed by green naghdi uniqueness is proved under

on the linear problem of swelling porous elastic soils in this paper we consider the linear theory of swelling porous elastic soils the formulation belongs to the theory of mixtures for porous elastic solids filled with fluid and gas it proposes some new mathematical difficulties logarithmic convexity and or the lagrange identity method is used in the case of fluid and gas saturation continuous results dependent on initial conditions and supply terms are obtained in the general case spatial decay estimates are also obtained by means of comparison arguments this last result is only valid when suitable conditions on the viscosity coefficients are satisfied

renormalization in the henon family i universality but non rigidity in this paper geometric properties of infinitely renormalizable real henon like maps f in mathbb r 2 are studied it is shown that the appropriately defined renormalizations r n f converge exponentially to the one dimensional renormalization fixed point the convergence to one dimensional systems is at a super exponen tial rate controlled by the average jacobian and a universal function a x it is also shown that the attracting cantor set of such a map has hausdorff dimension less than 1 but contrary to the one dimensional intuition it is not rigid does not lie on a smooth curve and generically has unbounded geometry

on a cahn hilliard allen cahn system coupled with a type iii heat equation and singular potentials abstract our aim in this article is to study the asymptotic behavior of a cahn hilliard allen cahn system coupled with a heat equation based on the type iii heat conduction law with singular potentials we also show further regularity results and we prove a strict separation property from the pure states in one space dimension

explosive instabilities in heat transmission a global non existence result is proved for a theory of heat propagation governed by a third order in time partial differential equation an upper bound for the length of the existence interval is derived

a re examination of the basic postulates of thermomechanics this paper is mainly concerned with a re examination of the basic postulates and the consequent procedure for the construction of the constitutive equations of material behaviour in thermomechanics however the implication of the basic postulates and the significance of the related procedure for the development of the constitutive equations is also illustrated in some detail in the context of flow of heat in a rigid solid with particular reference to the propagation of thermal waves at finite speed more specifically after briefly examining the nature of the basic equations of motion for a system of particles within the scope of the classical newtonian mechanics the basic postulates of the purely mechanical theory for a continuum including its specialization for a rigid body is re examined this includes some differences from the usual procedure on the subject next thermal variables are introduced and after observing a useful analogy between the thermal and mechanical variables a discussion of a theory of heat or a purely thermal theory is provided which differs from the usual development in the classical thermodynamics a detailed application of the latter development is then made to the problem of heat flow in a stationary rigid solid using several different and well motivated constitutive equations special cases of these include linearized theories of the classical heat flow by conduction and of heat flow transmitted as thermal waves the remainder of the paper is concerned with thermal mechanical theory of deformable media along with discussions of a number of related issues on the subject

growth decay and bifurcation of shock amplitudes under the type ii flux law by replacing fick s diffusion law with green and nagdhi s type ii flux law a hyperbolic counterpart to the classical fisherkpp equation is obtained in this article an analytical study of this pa

bounds for some non standard problems in porous flow and viscous green naghdi fluids a e green f r s and p m naghdi developed a new theory of continuum mechanics based on an entropy identity rather than an entropy inequality in particular within the framework of this theory they developed a new set of equations to describe viscous flow the new theory additionally involves vorticity and spin of vorticity we here derive energy bounds for a class of problem in which the initial data are given as a combination of data at time t 0 and at a later time t t such problems are in vogue in the mathematical literature and may be used for example to give estimates of solution behaviour in an improperly posed problem where one wishes to continue a solution backward in time in addition we derive similar energy bounds for a solution to the brinkman forchheimer equations of viscous flow in porous media

on the propagation of plane waves in type iii thermoelastic media the propagation of plane waves in infinite three dimensional type iii thermoelastic media is investigated exact dispersion relation solutions are determined and several characterizations of the wavefield are examined low and high frequency asymptotic expressions are given small coupling limit results are derived and special limiting cases including those corresponding to thermoelastic media of types ii and i are noted computational tools are used to illustrate the analytical findings and to study the effects of varying the physical parameters of the findings presented the following are most significant i the determination of critical values of the physical parameters and their impact on the wavefields ii ascertaining that type iii media behave essentially like type ii respectively type i media with respect to low respectively high frequency plane waves iii establishing the whitham stability of plane waves in type iii media and iv the determination of the dispersion characteristics of type iii media

some integrable subalgebras of the lie algebras of infinite dimensional lie groups this paper gives a proof of lie s second fundamental theorem in the context of infinite dimensional lie groups that is we define a class of lie subalgebras of the lie algebra of a large class of infinite dimensional lie groups say g which can be realized as the lie algebras of lie subgroups of g

on thermoelastic bodies with inner structure and microtemperatures abstract in the first part of this paper we present a linear theory of thermoelastic bodies with microstructure and microtemperatures which permits the transmission of heat as thermal waves at finite speed the theory is based on the entropy balance postulated by green and naghdi a e green p m naghdi a re examination of the basic postulates of thermomechanics proc r soc london a 432 1991 171 194 we consider bodies with microstructure whose microelements can stretch and contract independently of their translations then we establish existence and uniqueness results in the context of the dynamic theory

nonexistence of wandering domains for strongly dissipative infinitely renormalizable henon maps at the boundary of chaos this article generalizes the nonexistence of wandering domains from unimodal maps to infinitely period doubling renormalizable henon like maps in the strongly dissipative area contracting regime this solves an open problem proposed by van strien discrete contin dyn syst 27 2 557 588 2010 and lyubich and martens invent math 186 1 115 189 2011 we partition the phase space of a henon like map into two regions the good region and the bad region the good region is where the method of proof for unimodal maps applies to henon like maps while the bad region is where serious difficulties occur these difficulties are resolved by the two row lemma an inequality that relates the contraction of areas to the contraction of bad regions after analyzing the competition of the two types of contraction we show that the case of bad regions happens at most finitely many times and complete the proof as an application the theorem enriches our understanding of the topological structure of the heteroclinic web the union of the stable manifolds of periodic orbits forms a dense set in the domain

atomistic viewpoint of the applicability of microcontinuum theories abstract microcontinuum field theories including micromorphic theory microstructure theory micropolar theory cosserat theory nonlocal theory and couple stress theory are the extensions of the classical field theories for the applications in microscopic space and time scales they have been expected to overlap atomic model at microscale and encompass classical continuum mechanics at macroscale this work provides an atomic viewpoint to examine the physical foundations of those well established microcontinuum theories and to justify their applicability through lattice dynamics and molecular dynamics

hilbert schmidt groups as infinite dimensional lie groups and their riemannian geometry abstract we describe the exponential map from an infinite dimensional lie algebra to an infinite dimensional group of operators on a hilbert space notions of differential geometry are introduced for these groups in particular the ricci curvature which is understood as the limit of the ricci curvature of finite dimensional groups is calculated we show that for some of these groups the ricci curvature is

relations between the good definitions of compactness in l fuzzy topological spaces abstract in this paper we state the different definitions of compactness in l fuzzy topological spaces where l is a completely distributive lattice we obtain other characterizations of some of these notions and study them with respect to their goodness finally we establish the inter relations between the compactnesses which are good extensions we also obtain an improvement of our theorem 7 6 in 3

takens last problem and existence of non trivial wandering domains abstract in this paper we give an answer to a c r 2 r version of the open problem of takens in 42 which is related to historic behavior of dynamical systems to obtain the answer we show the existence of non trivial wandering domains near a homoclinic tangency which is conjectured by colli vargas 6 2 concretely speaking it is proved that any newhouse open set in the space of c r diffeomorphisms on a closed surface is contained in the closure of the set of diffeomorphisms which have non trivial wandering domains whose forward orbits have historic behavior moreover this result implies an answer in the c r category to one of the open problems of van strien 39 which is concerned with wandering domains for henon family

on the group of real analytic diffeomorphisms of a compact real analytic manifold in this paper we exhibit a lie group structure on the group of real analytic diffeomorphisms of a compact real analytic manifold further we show that a variant of the kupka smale theorem holds for the underlying topology of the above mentioned lie group introduction the overall objective of this work is to prove an analytic version of the kupka smale theorem given a smooth compact manifold m there exists a subset r c diff m which is a countable intersection of open dense subsets of diff r m so that if f c r and p is a periodic point of f of order n i e p ee pn f then i the eigenvalues of tp f n lie off the unit circle and ii the stable manifold ws p and unstable manifold wu p through p are injectively immersed further for p c pn f ws p and the unstable manifold wu q q c pm f m arbitrary intersect transversally symbolically ws p rhi wu q the significance of this theorem to the study of the stability problem in differential equations has been discussed by smale 16 this theorem has been extended to retarded functional differential equations 6 the proofs of these theorems known to me rely heavily on transversality theory which in turn relies heavily on the implicit function theorem for frechet differentiable functions defined in open subsets of banach spaces while this does not create a major theoretical difficulty in proving an analogue of the kupka smale theorem for diff m lim diff r m because of well known propositions concerning inverse r limits we have found that for m real analytic the path for proving an analogue of the kupka smale theorem is more circumlocutious the first problem we encountered was to find an appropriate natural topology for diff m our second set of problems was the discovery of a notion of differentiability in the context of our chosen topology for which an implicit function theorem holds which would be adequate for transversality theory the topology that we found natural turned out to be equivalent to the classical co topology studied by van hove 10 and j s e silva 15 that is an inductive limit of spaces of complex analytic functions colombeau 3 in an unpublished received by the editors january 13 1981 and in revised form september 28 1981 1980 mathematics subject classification primary 58f15 58h05 d1982 american mathematical society 0002 9947 81 0000 0095 07 00

convergence and structural stability in thermoelasticity we analyze the equations of thermoelasticity in a linear approximation first we prove that the solution depends continuously on changes in two thermal constants next we investigate how the solution of thermoelasticity of type iii converges to the solution of the usual thermoelasticity and to the solution of thermoelasticity without energy dissipation consequently we can also obtain an estimate of the approximation when we compare the classical thermoelasticity with thermoelasticity without energy dissipation last section investigates the structural stability in the class of thermoelasticity without energy dissipation

structural stability for the darcy equations of flow in porous media a priori bounds are derived for the darcy equations of flow in porous media when the porous body is subject to boundary conditions of newton cooling type with the aid of these a priori bounds we are able to demonstrate continuous dependence on the cooling coefficient when the boundary condition of newton cooling type is employed we further show that the solution depends continuously on a change in the equation of state employed in the body force in the darcy equation the model is allowed to change from one of boussinesq convection type to one more general and structural stability is established

an a priori error analysis of poro thermoviscoelastic problems abstract in this paper we study from the numerical point of view a dynamic one dimensional problem arising in thermoelasticity and thermoviscoelasticity of types ii and iii porosity is also included into the models the generic variational formulation leads to a coupled system written in terms of the velocity the volume fraction speed and the temperature fully discrete approximations are then introduced by using the finite element method and the implicit euler scheme a discrete stability property and a priori error estimates are proved finally some numerical examples are presented to demonstrate the numerical convergence of the algorithm the exponential decay of the discrete energy and the behavior of the solution

compact acoustic travelling waves in a class of fluids with nonlinear material dispersion we apply a phenomenological theory of continua put forth by rubin rosenau and gottlieb in 1995 to an important class of compressible media regarding the material characteristic length coefficient

the convenient setting for non quasianalytic denjoy carleman differentiable mappings abstract for quasianalytic denjoy carleman differentiable function classes c q where the weight sequence q q k is log convex stable under derivations of moderate growth and also an l intersection see 1 6 we prove the following the category of c q mappings is cartesian closed in the sense that c q e c q f g c q e f g for convenient vector spaces applications to manifolds of mappings are given the group of c q diffeomorphisms is a regular c q lie group but not better

rigidity for infinitely renormalizable area preserving maps the period doubling cantor sets of strongly dissipative henon like maps with different average jacobian are not smoothly conjugated as was shown previously the jacobian rigidity conjecture says that the period doubling cantor sets of two dimensional henon like maps with the same average jacobian are smoothly conjugated this conjecture is true for average jacobian zero for example the one dimensional case the other extreme case is when the maps preserve area for example when the average jacobian is one indeed the main result presented here is that the period doubling cantor sets of area preserving maps in the universality class of the eckmann koch wittwer renormalization fixed point are smoothly conjugated

inclusions and inhomogeneities in strain gradient elasticity with couple stresses and related problems abstract at small length scales and or in presence of large field gradients the implicit long wavelength assumption of classical elasticity breaks down postulating a form of second gradient elasticity with couple stresses as a suitable phenomenological model for small scale elastic phenomena we herein extend eshelby s classical formulation for inclusions and inhomogeneities while the modified size dependent eshelby s tensor and hence the complete elastic state of inclusions containing transformation strains or eigenstrains is explicitly derived the corresponding inhomogeneity problem leads to integrals equations which do not appear to have closed form solutions to that end eshelby s equivalent inclusion method is extended to the present framework in form of a perturbation series that then can be used to approximate the elastic state of inhomogeneities the approximate scheme for inhomogeneities also serves as the basis for establishing expressions for the effective properties of composites in second gradient elasticity with couple stresses the present work is expected to find application towards nano inclusions and certain types of composites in addition to being the basis for subsequent non linear homogenization schemes

a generalization of the caginalp phase field system with neumann boundary conditions abstract we study a generalized caginalp phase field system based on the theory of type iii heat conduction proposed by green and naghdi and supplemented with neumann boundary conditions in contrast to the dirichlet case the system exhibits a lack of dissipation on the thermal displacement variable however minus its spatial average is dissipative and we are able to prove the existence of the global attractor with optimal regularity for the associated semigroup

energy bounds for some non standard problems in thermoelasticity a e green f r s and p m naghdi developed two theories of thermoelasticity called type ii and type iii which are likely to be more natural candidates for the identification of a thermoelastic body than the usual theory we here derive energy bounds for a class of problem in which the initial data are given as a combination of data at time t 0 and at a later time t t such problems are in vogue in the mathematical literature and may be used for example to give estimates of solution behaviour in an improperly posed problem where one wishes to continue a solution backward in time

continuous dependence for the nonhomogeneous brinkman forchheimer equations in a semi infinite pipe abstract in this paper we consider the nonhomogeneous brinkman forchheimer equations in a semi infinite pipe continuous dependence for the brinkman forchheimer equations in a semi infinite pipe is obtained

spatial behavior for some non standard problems in linear thermoelasticity without energy dissipation in the present paper we consider a prismatic cylinder occupied by an anisotropic and homogeneous compressible linear thermoelastic material within the framework of the linear theory of thermoelasticity without energy dissipation the cylinder is subject to zero body force and heat supply and zero lateral specific boundary conditions and the motion is induced by a time dependent displacement and thermal displacement specified pointwise over the base further the motion is constrained such that the displacement thermal displacement velocity and temperature variation at points in the cylinder and at a prescribed time are in given proportions to but not identical with their respective initial values it is shown that certain integrals of the solution spatially evolve with respect to the axial variable conditions are derived that show the integrals exhibit alternative behavior and in particular for the semi infinite cylinder that there is either at least exponential growth or at most exponential decay provided the elasticity tensor is positive definite or strongly elliptic

on uniqueness and continuous dependence in type iii thermoelasticity abstract this note is concerned with the linear and linearised type iii thermoelastic theory proposed by green and naghdi first the continuous dependence of the solutions upon the initial data and supply terms is established for noncentrosymmetric bodies then a uniqueness result for centrosymmetric materials is established

energy bounds for some nonstandard problems in partial differential equations abstract we consider problems of the form d 2 u dt 2 au f u 0 u t g du dt 0 du dt t h for t 0 t where a is a densely defined linear time independent positive definite symmetric operator and and are constants although most of our results would hold for more general operators a we restrict attention to the case in which a is a differential operator and determine ranges of values of and for which it is possible to obtain energy bounds uniqueness results and in a special case pointwise bounds some extensions which include a damping term or a term which arises in a generalization of the kirchhoff string model are also discussed

the convenient setting for real analytic mappings we present here the cartesian closed theory for real analytic mappings it is based on the concept of real analytic curves in locally convex vector spaces a mapping is real analytic if it maps smooth curves to smooth curves and real analytic curves to real analytic curves under mild completeness conditions the second requirement can be replaced by real analytic along ane lines enclosed and necessary is a careful study of locally convex topologies on spaces of real analytic mappings as an application we also present the theory of manifolds of real analytic mappings the group of real analytic dieomorphisms of a compact real analytic manifold is a real analytic lie group

energy decay in a timoshenko type system of thermoelasticity of type iii in this paper we consider a one dimensional linear thermoelastic system of timoshenko type where the heat conduction is given by green and naghdi theories we prove the exponential stability by using the energy method

a note on discontinuity waves in type iii thermoelasticity two recent nonlinear theories of thermoelasticity developed by green and naghdi are examined it is shown that in type ii theory second sound is permissible and both mechanical and temperature waves may propagate in type iii theory we show that the situation is more analogous to that in classical nonlinear thermoelasticity one wave propagates and a homothermal temperature wave is allowed

a unified procedure for construction of theories of deformable media ii generalized continua in contrast to classical theories discussed in the accompanying paper part i the present paper deals exclusively with generalized continua a term that refers to a body embedded in a euclidean three dimensional space with each of its material points endowed with additional kinematic structure such generalized continua are conveniently identified here by cosserat or directed continua in which the additional structure is represented by independent director fields and the material domain of the body manifold is classified according to the four categories a a three dimensional volume b a two dimensional surface c a one dimensional space curve and d a point in the derivation of a thermomechanical theory for each of these categories we use the same unified procedure as in part i but now the various energies that enter the balance of energy must be modified to include additional kinetic ingredients new theories of this kind have increasingly provided over the last three decades effective means of formulating and studying new behaviour of materials in both fluid and solid mechanics that were not previously possible by the classical theories our attention is first focused in the development of the theory for the first category and this is discussed in two stages first for a cosserat continuum with a single director and then for n directors our derived results include for the first time a derivation from the balance of energy of balances of director momenta and balances of entropies in the presence of more than one independent temperature field the treatments of categories b to d are somewhat shorter since their developments are formally similar to that of category a

the convergence of non newtonian fluids to navier stokes equations abstract in this paper the convergence of solutions for incompressible dipolar viscous non newtonian fluids is investigated we obtain the conclusion that the solutions of non newtonian fluids converge to the solutions of navier stokes equations in the sense of l 2 norm resp h 1 norm as the viscosities tend to zero and the initial data belong to h 1 resp h 2 moreover we obtain l norm convergence of solutions if the initial data belong to h 2

period doubling bifurcations for families of maps on ℝ n infinite sequences of period doubling bifurcations in one parameter families 1 pf of maps enjoy very strong universality properties this is known numerically in a multitude of cases and has been shown rigorously for certain 1 pf of maps on the interval these bifurcations occur in 1 pf of analytic maps at values of the parameter tending to a limit with the asymptotically geometric ratio 1 4 6692 in this paper we indicate the main steps of a proof that the same is true for 1 pf of analytic maps from n to n whose restriction to n is real

strain gradient theory of chiral cosserat thermoelasticity without energy dissipation in this paper we use the green naghdi theory of thermomechanics of continua to derive a linear strain gradient theory of cosserat thermoelastic bodies the theory is capable of predicting a finite speed of heat propagation and leads to a symmetric conductivity tensor the constitutive equations for isotropic chiral thermoelastic materials are presented in this case in contrast with the classical cosserat thermoelasticity a thermal field produces a microrotation of the particles the thermal field is influenced by the displacement and microrotation fields even in the equilibrium theory existence and uniqueness results are established the theory is used to study the effects of a concentrated heat source in an unbounded homogeneous and isotropic chiral solid

on the impossibility of localization in linear thermoelasticity in the middle of the 1990s green naghdi proposed three theories of thermoelasticity that they labelled as types i ii and ii the type ii theory which is also called thermoelasticity without energy dissipation is conservative and the solutions cannot decay with respect to time it is well known that in general in the linear theories of thermoelasticity of types i and iii the solutions decay with respect to time in many situations this decay is at least exponential in this paper we study whether this decay can be fast enough to guarantee the solutions to be zero in a finite time we investigate the impossibility of the localization in time of the solutions of linear thermoelasticity for the theories of green naghdi this means that the only solution that vanishes after a finite time is the null solution the main idea is to show the uniqueness of solutions for the backward in time problem to be precise for type iii thermoelasticity we will prove the impossibility of localization of solutions in the case of bounded domains and for the type i thermoelasticity in the case of exterior domains even when the solutions can be unbounded whether the spatial variable goes to infinity

on the concept of attractor this note proposes a definition for the concept of attractor based on the probable asymptotic behavior of orbits the definition is sufficiently broad so that every smooth compact dynamical system has at least one attractor

crystal dissolution and precipitation in porous media pore scale analysis in this paper we discuss a pore scale model for crystal dissolution and precipitation in porous media we consider first general domains for which existence of weak solutions is proven for the particular case of strips we show that free boundaries occur in the form of dissolution precipitation fronts as the ratio between the thickness and the length of the strip vanishes we obtain the upscaled reactive solute transport model proposed in 12

renormalization in the henon family ii the heteroclinic web we study highly dissipative henon maps f c b x y mapsto c x 2 by x with zero entropy they form a region in the parameter plane bounded on the left by the curve w of infinitely renormalizable maps we prove that morse smale maps are dense in but there exist infinitely many different topological types of such maps even away from w we also prove that in the infinitely renormalizable case the average jacobian bf on the attracting cantor set mathcal o f is a topological invariant these results come from the analysis of the heteroclinic web of the saddle periodic points based on the renormalization theory along these lines we show that the unstable manifolds of the periodic points form a lamination outside mathcal o f if and only if there are no heteroclinic tangencies

decay of solutions for a mixture of thermoelastic solids with different temperatures we study a system modeling thermomechanical deformations for mixtures of thermoelastic solids with two different temperatures that is when each component of the mixture has its own temperature in particular we investigate the asymptotic behavior of the related solutions we prove the exponential stability of solutions for a generic class of materials in case of the coupling matrix b being singular we find that in general the corresponding semigroup is not exponentially stable in this case we obtain that the corresponding solution decays polynomially as t 1 2 in case of neumann boundary condition additionally we show that the rate of decay is optimal for dirichlet boundary condition we prove that the rate of decay is t 1 6 finally we demonstrate the impossibility of time localization of solutions in case that two coefficients related with the thermal conductivity constants agree

birth of homoclinic intersections a model for the central dynamics of partially hyperbolic systems creation d intersection homoclines un modele pour la dynamique centrale des systemes partiellement hyperboliques nous montrons une conjecture de j palis tout diffeomorphisme d une variete compacte peut etre approche en topologie c 1 par un diffeomorphisme morse smale ou par un diffeomorphisme ayant une intersection homocline transverse