hascasl integrated higher order specification and program development we lay out the design of hascasl a higher order extension of the algebraic specification language casl that serves both as a wide spectrum language for the rigorous specification and development of software in particular but not exclusively in modern functional programming languages and as an expressive standard language for higher order logic distinctive features of hascasl include partial higher order functions higher order subtyping shallow polymorphism and an extensive type class mechanism moreover hascasl provides dedicated specification support for monad based functional imperative programming with generic side effects including a monad based generic hoare logic

a functorial semantics for multi algebras and partial algebras with applications to syntax multi algebras allow for the modelling of nondeterminism in an algebraic framework by interpreting operators as functions from individual arguments to sets of possible results we propose a functorial presentation of various categories of multi algebras and partial algebras analogous to the classical presentation of algebras over a signature as cartesian functors from the algebraic theory over to set we introduce two different notions of theory over a signature both having a structure weaker than cartesian and we consider functors from them to rel or pfn the categories of sets and relations or partial functions respectively next we discuss how the functorial presentation provides guidelines when choosing syntactical notions for a class of algebras and as an application we argue that the natural generalization of usual terms are conditioned terms for partial algebras and term graphs for multi algebras

algebraic theories of quasivarieties abstract analogously to the fact that lawvere s algebraic theories of finitary varieties are precisely the small categories with finite products we prove that i algebraic theories of many sorted quasivarieties are precisely the small left exact categories with enough regular injectives and ii algebraic theories of many sorted horn classes are precisely the small left exact categories with enough m injectives where m is a class of monomorphisms closed under finite products and containing all regular monomorphisms we also present a gabriel ulmer type duality theory for quasivarieties and horn classes

the space of omega limit sets of a continuous map of the interval we first give a geometric characterization of limit sets we then use this characterization to prove that the family of limit sets of a continuous interval map is closed with respect to the hausdorff metric finally we apply this latter result to other dynamical systems

holder classes with boundary conditions as interpolation spaces on etudie la caracterisation de certains espaces d interpolation reels entre le domaine d un operateur differentiel elliptique avec des conditions aux limites generales et l espace de banach de fonctions continues dans lequel le domaine est plonge

transmission problems in a thin layer set in the framework of the holder spaces resolution and impedance concept abstract we consider a family of singular transmission problems depending on some small positive parameter set in the juxtaposition of two rectangular domains they are written in the form of abstract elliptic equations and the study here is given in the holder spaces completing in this way the work in lp cases given in a favini r labbas k lemrabet s maingot study of the limit of transmission problems in a thin layer by the sum theory of linear operators rev mat complut 18 1 2005 143 176 in this first part we present a new approach for the resolution of these problems by using the concept of impedance operator this method is different of the one performing a rescaling in the thin layer see a favini r labbas k lemrabet s maingot study of the limit of transmission problems in a thin layer by the sum theory of linear operators rev mat complut 18 1 2005 143 176 it leads to obtain direct and simplified problems we use the dunford calculus and some techniques similar to that in r labbas problemes aux limites pour une equation differentielle abstraite de type elliptique these d etat universite de nice 1987 a favini r labbas s maingot h tanabe a yagi unified study of elliptic problems in holder spaces c r math acad sci paris 134 2005 g dore a favini r labbas k lemrabet s maingot a transmission problem in a thin layer part i sharp estimates in press to prove existence uniqueness results and some specific estimates on the impedance operator this study will allow us in a forthcoming work to obtain respectively optimal regularities and the limit problem when 0

optimal control problems for the equation of motion of membrane with strong viscosity optimal control problems are studied for the equation of membrane with strong viscosity the g teaux differentiability of solution mapping on control variables is proved and the various types of necessary optimality conditions corresponding to the distributive and terminal values observations are established

stationary navier stokes equations with critically singular external forces existence and stability results abstract we show the unique existence of solutions to stationary navier stokes equations with small singular external forces belonging to a critical space to the best of our knowledge this is the largest critical space that is available up until now for this kind of existence this result can be viewed as the stationary counterpart of the existence result obtained by h koch and d tataru for the free non stationary navier stokes equations with initial data in bmo 1 the stability of the stationary solutions in such spaces is also obtained by a series of sharp estimates for resolvents of a singularly perturbed operator and the corresponding semigroup

nonlinear analytic semiflows in this paper a local existence and regularity theory is given for nonlinear parabolic initial value problems x t f x t and quasilinear initial value problems x t a x t x t f x t this theory extends the theory of daprato and grisvard of 1979 and shows how various properties like analyticity of solutions can be derived as a direct corollary of the existence theorem

on some nonlinear hyperbolic systems with damping boundary conditions in recent years the effect of boundary damping on the solutions to interior initial boundary value problems for hyperbolic equations has been extensively studied in 111 quinn and russell considered the wave equation with damping boundary condition on a part of the boundary it was proved by control theoretic method that if the boundary where the boundary condition was posed was star shaped then the solution of the wave equation had polynomial decay rate later on chen in l got the exponential decay of solutions to the wave equation under the more restrictive assumptions on the boundary and also lagnese in 6 got the exponential decay of solutions to the three dimensional elastic wave equations with damping boundary condition on a part of the boundary provided the geometry of the boundary is suitably restricted as for the nonlinear problem greenberg and li in 131 considered the nonlinear conservation system in one space dimension with damping boundary condition and proved the global existence of smooth solution when the initial data are small shen and zheng 14 and nagasawa 9 proved the global existence of classical solutions to the system of one dimensional thermoelasticity and to the system of one dimensional nonlinear problem in higher space dimension respectively for the nonlinear problem in higher space dimension to our knowledge the works were done by qin lo and zajaczkowski 26 only for the nonlinear wave equation with damping boundary conditions based on chen s results in l in this paper our aim is to derive the decay rate of solutions to the linear hyperbolic system of second order with damping boundary condition without any assumptions on the geometry of the boundary by using the spectral analysis method cf section 2 below and then to prove the global existence of smooth solutions to the corresponding nonlinear system with applications to nonlinear elastodynamics and to nonlinear acoustic wave equations our approach to obtaining the rate of decay of solutions to linear problem is completely different from l 6 and lo

on a global existence theorem of small amplitude solutions for nonlinear wave equations in an exterior domain soit un domaine non borne dans un espace euclidien a n dimensions r n a frontiere compacte et c on considere le probleme mixte u u f t x d 1 d 1 u f t x dans 0 u 0 sur 0 u 0 x u 0 x t u 0 x u 1 x dans f est une fonction non lineaire a valeur reelle et d 1 d 1 u t j x u 1 j 2

restriction categories ii partial map classification an algebraic characterization of monads which are abstract partial map classifiers is provided without the assumption that the categories of total maps possess products by an abstract partial map classifier we mean a monad whose kleisli category is a full subcategory of a partial map category wherein the induced comonad classifies partial maps in the usual sense a construction of the corresponding actual partial map classifier from an abstract one is described and conditions for an abstract partial map classifier to be a real one are provided the paper uses the notion of a restriction category developed in earlier work and the characterization of these as full subcategories of partial map categories

matrix methods for wave equations in analogy to a characterisation of operator matrices generating c0 semigroups due to r nagel 13 we give conditions on its entries in order that a 2 2 operator matrix generates a cosine operator function we apply this to systems of wave equations to second order initial boundary value problems and to overdamped wave equations

on a class of retarded partial differential equations on developpe des resultats recents sur des equations d evolution abstraites afin de les appliquer a un type d equations dans des espaces de banach avec un retard discret et continu ces equations peuvent etre considerees comme la version abstraite d equations integrodifferentielles partielles a retard

on the evolution operator for a class of non autonomous abstract parabolic equations abstract we state existence and several properties of the evolution operator relevant to a family a t 0 t t of generators of analytic semigroups in a banach space the assumption that certain interpolation spaces do not depend on t allows us to weaken the usual regularity hypotheses on t a t requiring only continuity in suitable topologies

global solutions of abstract quasilinear parabolic equations abstract local and global existence and uniqueness for strict solutions of abstract quasilinear parabolic equations are studied applications to quasilinear parabolic partial differential equations are also given

global smooth solutions and asymptotic stability in one dimensional nonlinear thermoelasticity the global existence of smooth solutions to the equations of nonlinear thermoelasticity is shown for a one dimensional homogeneous reference configuration dirichlet boundary conditions are studied and the asymptotic behaviour of the solutions as t is described

quasilinear systems with memory kernels we consider a quasilinear integrodifferential system in non normal form such a system is a generalization of a phase field model with memory and includes as a particular case the system describing the combustion of a material with memory in this paper we study both the direct and the inverse problems our fundamental tools are the theory of analytic semigroups optimal regularity results and fixed point arguments

analysis of fully discrete approximations to parabolic problems with rough or distribution valued initial data we consider fully discrete approximations to a parabolic initial boundary value problem with rough or distribution valued initial data in two space dimensions for discretization in time and space we apply single step methods and the standard galerkin method with piecewise linear test functions respectively for spatial discretization of the initial condition we are however forced to use more involved constructions our main result is stability and error estimates of the discrete solutions

global existence of weak solutions for two dimensional semilinear wave equations with strong damping in an exterior domain abstract we consider two dimensional mixed problems in an exterior domain for a semilinear strongly damped wave equation with a power type nonlinearity u p if the initial data have a small weighted energy we shall derive a global existence and energy decay results in the case when the power p of the nonlinear term satisfies p 6

existence and non existence of global solutions to initial boundary value problems for nonlinear evolution equations with strong dissipation abstract the main purpose in this paper is to investigate existence and non existence of global solutions of the initial dirichlet boundary value problem for evolution equations with strong dissipation many authors studied classes consisting of such types of equations for which initial boundary value problems possess global solutions for this purpose we consider a related problem and seek global solutions and blow up solutions of it depending on whether it belongs to such classes or not

a new numerical method for backward parabolic problems in the maximum norm setting a new method for solving numerically backward parabolic problems is proposed as usual for this kind of ill posed problems it is assumed that an a priori bound for the solution is available the algorithm consists of two basic steps first a standard forward integration is performed in order to approximate the solution at suitable future time levels second a holomorphic recovery procedure is carried out providing the required approximations for the preceding times the analysis is valid in the maximum norm setting and rigorous estimates are derived among other advantages the method can also be applied to nonlinear problems and it produces a continuous output some numerical illustrations are presented

global existence and exponential stability of small solutions to nonlinear viscoelasticity the global existence of smooth solutions to the equations of nonlinear hyperbolic system of 2nd order with third order viscosity is shown for small and smooth initial data in a bounded domain ofn dimensional euclidean space with smooth boundary dirichlet boundary condition is studied and the asymptotic behaviour of exponential decay type of solutions ast tending to is described time periodic solutions are also studied as an application of our main theorem nonlinear viscoelasticity strongly damped nonlinear wave equation and acoustic wave equation in viscous conducting fluid are treated

direct and inverse problems for a phase field model with memory we consider a semilinear integrodifferential system in non normal form such a system is a generalization of the one that arises in the phase field theory with memory we prove an abstract existence and uniqueness theorem and a continuous dependence result for the direct problem reformulating the direct problem in a suitable way we prove that the identification problem admits a unique solution

asymptotic expansion for layer solutions of a singularly perturbed reaction diffusion system for a singularly perturbed n dimensional system of reactiondiffusion equations assuming that the 0th order solutions possess boundary and internal layers and are stable in each regular and singular region we construct matched asymptotic expansions for formal solutions in all the regular boundary internal and initial layers to any desired order in e the formal solution shows that there is an invariant manifold of wave front like solutions that attracts other nearby solutions we also give conditions for the wave front like solutions to converge slowly to stationary solutions on that manifold

regular solutions for time dependent abstract integrodifferential equations with singular kernel abstract results of existence uniqueness and regularity for strict and classical solutions of linear nonautonomous integrodifferential initial value problems are proved using maximal regularity properties for the autonomous nonintegral case

on the solutions of the first boundary value problem for the linear parabolic equations on etudie le premier probleme aux valeurs limites pour une equation parabolique lineaire d ordre 2 sous l hypothese que le terme inhomogene est continu en espace et en temps et continu de holder seulement par rapport aux variables d espace

an equational notion of lifting monad we introduce the notion of an equational lifting monad a commutative strong monad satisfying one additional equation valid for monads arising from partial map classifiers we prove that any equational lifting monad has a representation by a partial map classifier such that the kleisli category of the former fully embeds in the partial category of the latter thus equational lifting monads precisely capture the equational properties of partial maps as induced by partial map classifiers the representation theorem also provides a tool for transferring nonequational properties of partial map classifiers to equational lifting monads it is proved using a direct axiomatization of kleisli categories of equational lifting monads this axiomatization is of interest in its own right

well posedness and attractor on the 2d kirchhoff boussinesq models abstract the paper studies the well posedness and the existence of attractors for a class of 2d kirchhoff boussinesq models u t t k u t 2 u d i v u 1 u 2 g u with 0 0 0 we show that i the ibvp of the equations is well posed in natural energy space x 2 and strong solution space x 4 respectively provided that g s c 1 s 2 ii the related solution semigroup has a global and an generalized exponential attractor in x 2 provided that the damping parameter k is suitably large and g s c iii in particular when 0 the corresponding boussinesq model has a subclass j of limit solutions and the subclass j has a weak global attractor in energy space x 1 without any upper bound restriction for the growth exponent of g u iv in the cases that either 0 or 0 the corresponding model has a global attractor in x 4 provided that g s c 1 s and without any restriction for the damping parameter k 0 especially when 0 the corresponding results extend those in grassell et al 2009

a simple characterization of theories of varieties abstract we answer the question of which theories in the sense of gabriel and ulmer give rise to finitary multi sorted varieties and exhibit the 2 category of varieties as a non full bireflective sub 2 category of the 2 category of locally finitely presentable categories a central role is played by those objects which we call effective projectives whose hom functors preserve coequalizers of reflexive graphs

some results on locally finitely presentable categories we prove that any full subcategory of a locally finitely presentable l f p category having small limits and filtered colimits preserved by the inclusion functor is itself l f p here full may be weakened to full with respect to isomorphisms further we characterize those left exact functors i c d between small categories with finite limits for which the functor i lex d set lex c set induced by composition is full and faithful as an application we prove a theorem on sheaf representations a consequence of which is that for any site c c j on a category c with finite limits defined by a subcanonical grothendieck topology j the closure in lex c set under small limits and filtered colimits of the models of c is the whole of lex c set introduction in this paper we make contributions to the logic of essentially algebraic theories although the terminology will be categorical the motivation is a model theoretical one our interest lies in arriving at results connecting the syntax and the semantics of that logic the definition of essentially algebraic theory can be given conveniently only in categorical terms as is usually done we identify such a theory with a small category having all finite limits the 2 category of all such categories with functors preserving finite limits as morphisms 1 cells and all natural transformations as 2 cells is denoted by lex lex denotes the 2 category with the smallness restriction removed set the category of small sets is the standard theory an object of lex a model of a theory c e lex is a morphism c set in lex lex c set is the category of models of c talking about relations of syntax and semantics amounts roughly to relating c and lex c set following kr we could call our subject the doctrine of cartesian logic the doctrine of cartesian logic corresponds to a logic with existential quantification restricted to cases when unique existence is assured for a detailed account of this correspondence cf c the main fact of the correspondence can be stated simply call a first order theory t over a language l axiomatized by sentences of the form vx p x 3 y0 x y with p and finite conjunctions of atomic formulas 3 1y means there is a unique y such that a lim theory then the categories of models of lim theories with ordinary homomorphisms as morphisms are the same as the categories lex c set for c c lex the connection of the lim theories themselves and objects of lex is a bit less easy to state it is done in c received by the editors may 8 1984 and in revised form april 20 1985 1980 mathematics subject classification 1985 revision primary 03g30 18b99 secon lary 03c20 03c52 d1987 american mathematical society 0002 9947 87 1 00 25 per page

the cauchy problem for time dependent abstract parabolic equations of higher order after the pioneering works by chazarain 2 and dubinskii 3 in the early seventies several papers were devoted to higher order differential equations in a banach space especially for either constant coefficient or second order equations detailed references can be find in 4 sect 25 c very recent results in the constant coefficient case are due to sandefur s for second order semilinear equations and to neubrander s for linear arbitrary order equations in a recent paper 7 we considered an equation such as

nonlinear second order equations with applications to partial differential equations where a and b are usually unbounded linear operators in a banach space these problems arise often in the study of partial differential equations as is usual we control a nonlinear perturbation possibly involving spatial derivatives by the linear terms which contain higher order spatial derivatives but contrary to the usual method of reducing the problem to a first order system in some energy norm space as in 9 5 we use the factoring method of lo this method allows the equation to be written as an integral equation containing a double integral involving the nonlinearity reflecting the fact that the equation is second order there are several advantages to this approach which will be illustrated fully in the examples first we show that the equation is locally well posed if loosely the nonlinearity satisfies the local lipschitz condition

finite dimensional attractors for the quasi linear strongly damped wave equation abstract we present a new method of investigating the so called quasi linear strongly damped wave equations t 2 u t x u x u f u x x u g in bounded 3d domains this method allows us to establish the existence and uniqueness of energy solutions in the case where the growth exponent of the non linearity is less than 6 and f may have arbitrary polynomial growth rate moreover the existence of a finite dimensional global and exponential attractors for the solution semigroup associated with that equation and their additional regularity are also established in a particular case 0 which corresponds to the so called semi linear strongly damped wave equation our result allows to remove the long standing growth restriction f u c 1 u 5

local existence of solutions to the initial value problem for one dimensional strain limiting viscoelasticity abstract in this work we prove local existence of strong solutions to the initial value problem arising in one dimensional strain limiting viscoelasticity which is based on a nonlinear constitutive relation between the linearized strain the rate of change of the linearized strain and the stress the model is a generalization of the nonlinear kelvin voigt viscoelastic solid under the assumption that the strain and the strain rate are small we define an initial value problem for the stress variable and then under the assumption that the nonlinear constitutive function is strictly increasing we convert the problem to a new form for the sum of the strain and the strain rate using the theory of variable coefficient heat equation together with a fixed point argument we prove local existence of solutions finally for several constitutive functions widely used in the literature we show that the assumption on which the proof of existence is based is not violated

on the abstract cauchy problem of parabolic type in spaces of continuous functions on etudie l existence l unicite et les proprietes de regularite des solutions du probleme de cauchy u t au r f t o t t u o u 0 ou a d a ce e est un operateur lineaire clos dans l espace de banach e

quasilinear evolution equations and parabolic systems it is shown that general quasilinear parabolic systems possess unique maximal classical solutions for sufficiently smooth initial values provided the boundary conditions are time independent moreover it is shown that in the autonomous case these equations generate local semi flows on appropriate sobolev spaces our results apply in particular to the case of prescribed boundary values dirichlet boundary conditions

holder regularity in variational parabolic non homogeneous equations abstract we prove optimal holder regularity results for the solutions to second order variational parabolic equations with holder continuous coefficients and non homogeneous boundary data using analytic semigroups methods

large time behavior of solutions for the nonlinear wave equation with viscosity in odd dimensions abstract we study the dissipation of solutions of the cauchy problem for the nonlinear dissipative wave equation in odd multi spatial dimensions pointwise estimates of the time asymptotic shape of the solutions are obtained and shown to exhibit the generalized huygens principle our approach is based on the detailed analysis of the green function of the linearized system this is used to study the coupling of nonlinear diffusion waves

restriction categories i categories of partial maps given a category with a stable system of monics one can form the corresponding category of partial maps to each map in this category there is on the domain of the map an associated idempotent which measures the degree of partiality this structure is captured abstractly by the notion of a restriction category in which every arrow is required to have such an associated idempotent categories with a stable system of monics functors preserving this structure and natural transformations which are cartesian with respect to the chosen monics form a 2 category which we call mcat the construction of categories of partial maps provides a 2 functor par mcat cat we show that par can be made into an equivalence of 2 categories between mcat and a 2 category of restriction categories the underlying ordinary functor par r0 mcat 0 ca t0 of the above 2 functor par turns out to be monadic and from this we deduce the completeness and cocompleteness of the 2 categories of m categories and of restriction categories we also consider the problem of how to turn a formal system of subobjects into an actual system of subobjects a formal system of subobjects is given by a functor into the category slat of semilattices this structure gives rise to a restriction category which via the above equivalence of 2 categories gives an m category this m category contains the universal realization of the given formal subobjects as actual subobjects

recovering a leading coefficient and a memory kernel in first order integro differential operator equations abstract we are concerned with the identification of the scalar functions a and k in the convolution first order integro differential equation u t a t au t k bu t f t 0 t t k v t 0 t k t s v s ds in a banach space x where a and b are linear closed operators in x a being the generator of an analytic semigroup of linear bounded operators taking advantage of two pieces of additional information we can recover under suitable assumptions and locally in time both the unknown functions a and k the results so obtained are applied to an n dimensional integro differential identification problem in a bounded domain in r n

global existence of small solutions to a class of nonlinear evolution equations on etudie le comportement global des solutions d une classe d equations d evolution non lineaires on considere le probleme aux valeurs initiales pour des equations quasilineaires qui sont des perturbations d equations lineaires dissipatives

cauchy problem for quasi linear wave equations with nonlinear damping and source terms abstract the paper studies the existence and non existence of global weak solutions to the cauchy problem for a class of quasi linear wave equations with nonlinear damping and source terms it proves that when max m p where m 1 1 and p 1 are respectively the growth orders of the nonlinear strain terms the nonlinear damping term and the source term under rather mild conditions on initial data the cauchy problem admits a global weak solution especially in the case of space dimension n 1 the weak solutions are regularized and so generalized and classical solution both prove to be unique on the other hand if 0 1 and the initial energy is negative then under certain opposite conditions any weak solution of the cauchy problem blows up in finite time and an example is shown

maximum norm analysis of completely discrete finite element methods for parabolic problems we consider full discretizations of linear parabolic initial value problems in any space dimension finite elements are used for the discretization in space the resulting semidiscrete problem is integrated in time by means of a strongly a theta acceptable rational method stability estimates are derived and error bounds are established in the maximum norm for both smooth and rough initial data

global existence of solutions for a strongly coupled quasilinear parabolic system we are interested in existence uniqueness and a priori estimates of non negative solutions to the following problem begin gathered u t delta left left 1 alpha v right u right uf u v hfill v t delta v vg u v quad in 0 infty times omega hfill u v 0 quad in 0 infty times partial omega hfill u 0 u 0 v 0 v 0 quad in omega hfill end gathered 1 0

initial boundary value problems for the equations of motion of compressible viscous and heat conductive fluids the equations of motion of compressible viscous and heat conductive fluids are investigated for initial boundary value problems on the half space and on the exterior domain of any bounded region the global solution in time is proved to exist uniquely and approach the stationary state ast provided the prescribed initial data and the external force are sufficiently small

integrated semigroups and higher order abstract equations abstract let e be a banach space b 0 b n 1 closed linear operators on e and f 0 e this paper is devoted to the study of well posedness of the cauchy problem for higher order abstract differential equations formula using the theory of integrated semigroups we obtain some concise and useful criteria

the hascasl prologue categorical syntax and semantics of the partial λ calculus we develop the semantic foundations of the specification language hascasl which combines algebraic specification and functional programming on the basis of moggi s partial calculus generalizing lambek s classical equivalence between the simply typed calculus and cartesian closed categories we establish an equivalence between partial cartesian closed categories pccc s and partial theories building on these results we define set theoretic notions of intensional henkin model and syntactic algebra for moggi s partial calculus these models are shown to be equivalent to the originally described categorical models in pccc s via the global element construction the semantics of hascasl is defined in terms of syntactic algebras correlations between logics and classes of categories facilitate reasoning both on the logical and on the categorical side as an application we pinpoint unique choice as the distinctive feature of topos logic in comparison to intuitionistic higher order logic of partial functions which by our results is the logic of pccc s with equality finally we give some applications of the model theoretic equivalence result to the semantics of hascasl and its relation to first order casl

analyticity of the maximal solution of an abstract nonlinear parabolic equation where u t x 0 7 j x r r satisfies other suitable conditions problem p is studied under the assumption that af au generates an analytic semigroup in e and has domain f which corresponds to a parabolicity condition on equation p problems of this kind have been studied by monotonicity methods see brezis 111 crandall ligget 3 and crandall pazy 4 to obtain global but weak solutions of p here we find a maximally defined strict solution by means of a linearization method and by virtue of maximal regularity results for the linear case this method has been used by da prato grisvard in 5 to obtain strict solutions of p with arguments which seem to be more simple and suitable to our purpose we get also the analyticity of u with respect to 1 w when f is analytic in section 1 some notation and assumptions are given problem p is studied in section 2 where we prove existence and uniqueness of the strict solution of p which is defined on a maximal time interval contained in 0 t and it is continuous with respect to t 0 in section 3 we give conditions to get global existence of the solution in section 4 we study analyticity with respect to t ug of the maximally defined solution of p and in section 5 a simple example is given in a subsequent paper we will show how this theory applies to the study of the analyttctty of the solutions of nonlinear parabol ic partial differential equations in spaces of holder continuous functions

on linear volterra equations of parabolic type in banach spaces linear integrodifferential equations of volterra type in a banach space are studied in case the main part of the equation generates an analytic co semigroup under very general assumptions it is shown that a resolvent operator exists and that many of the solution properties of parabolic evolu tion equations are inherited the results are then applied to integro partial differential equations of parabolic type

categories of partial maps abstract this paper attempts to reconcile the various abstract notions of category of partial maps which appear in the literature first a particular algebraic theory p categories is introduced and a representation theorem proved this gives the authors a coherent framework in which to place the various other definitions both algebraic theories and theories which make essential use of the poset enriched structure of partial maps are discussed proofs of equivalence are given where possible and counterexamples where known the paper concludes with brief sections on the representation of partial maps and on partial algebras

limiting behavior for strongly damped nonlinear wave equations in this paper we investigate both the existence and the limiting behavior for the equation utt aut au t u ut where a is a sectorial operator is periodic in t and satisfies certain regularity and growth assumptions in most results on limiting behavior we will assume a has compact resolvent we consider the equation as an abstract ode defined on a paired space x x 0 1 with regard to the limiting behavior one of our principal results will be to show that if there is a bounded set in one of the spaces considered for which all points or trajectories enter into and remain then there is a set j consisting of very smooth functions defined on all of the spaces considered which is the maximum compact invariant set uniformly asymptotically stable connected and having very strong attractivity properties in all these spaces we will often show it attracts all points in a bounded set uniformly we will give a few sharper results for the case where a the work is motivated by recent papers of webb and fitzgibbon and applies techniques found in recent papers by the author

global and blow up solutions for a quasilinear hyperbolic equation with strong damping abstract in this paper we study a quasilinear hyperbolic equation with strong damping firstly by use of the successive approximation method and a series of classical estimates we prove the local existence and uniqueness of a weak solution secondly via some inequalities the potential method and the concave method we derive the asymptotic and blow up behavior of the weak solution with different conditions

analytic semigroups generated by ultraweak operators let be a regular open subset of r n we present an improved generation result for nonvariational operators in l 1 this result is obtained by studying ultraweak operators and by proving generation of analytic semigroups in l p l p and in we also characterise interpolation and extrapolation spaces

on the continuity of ornstein uhlenbeck processes in infinite dimensions existence and continuity of ornstein uhlenbeck processes in banach and hilbert spaces are investigated under various assumptions

wave equations with strong damping in hilbert spaces abstract we study the cauchy problem for abstract dissipative equations in hilbert spaces generalizing wave equations with strong damping terms in r n or exterior domains our main result is a generalized diffusion phenomenon the long time asymptotics of strongly damped wave equations is a combination of solutions of diffusion and wave equations in particular we obtain sharp decay estimates the proofs rely on the energy method in the fourier space and its generalization based on the spectral theorem for self adjoint operators

global solutions of nonlinear hyperbolic equations for small initial data on considere des systemes quasilineaires d equations hyperboliques d ordre 2 qui sont des deformations non lineaires de l equation d onde on etudie l existence globale et le comportement asymptotique des solutions du probleme de cauchy quand la donnee initiale est suffisamment petite

non explosion boundedness and ergodicity for stochastic semilinear equations abstract sufficient conditions for non explosion boundedness and ergodicity of solutions of a class of semilinear stochastic equations are given applications of the results are based on a new regularity theorem for solutions of the linear problem

uniform decay estimates and the lorentz invariance of the classical wave equation on etudie le comportement asymptotique des solutions de u 0 ou t 2 1 2 n 2 pour des conditions initiales u 0 u t g x en t 0 avec g reguliere a support compact dans r n

universality with respect to ω limit sets abstract a discrete dynamical system on a compact metric space x is called universal with respect to limit sets if among its limit sets there is a homeomorphic copy of any limit set of any dynamical system on x by a result of pokluda and smital the unit interval admits a universal system in this paper we study the problem of the existence of universal systems on cantor spaces graphs dendrites and higher dimensional spaces

global existence of small solutions to nonlinear evolution equations abstract we study the global existence and asymptotic behaviour of small solutions of a large class of nonlinear partial differential equations if the nonlinear terms are of high degree the solutions will be asymptotic to solutions of the linear equation

global and blow up solutions for a system of nonlinear hyperbolic equations with dissipative terms abstract in this paper we study a nonlinear hyperbolic system with strong damping firstly by use of the successive approximation method and a series of classical estimates we prove the local existence and uniqueness of weak solution secondly via some inequalities applying the potential method and the concave method we discuss the asymptotic and blow up behavior of weak solution with different conditions

existence of a global solution for a viscoelastic system in this paper a unique classical solution v u of the cauchy problem 1 2 is obtained if v 0 x 1 alpha less than or equal to m u 0 x 2 alpha less than or equal to m the a priori estimates v x t 1 alpha u x t 2 alpha less than or equal to m t are obtained by using the maximum principle without the restriction lim x infinity v 0 x u 0 x v u where v u are constants this resolves a problem proposed by j a smeller shock waves and reaction diffusion equations p 444 springer verlag new york berlin 1982 for the viscoelastic system a parallel result theorem 8 for a model 42 of compressible adiabatic flow through porous media with a physical viscosity is also obtained c 1998 academic press

partiality cartesian closedness and toposes presentation equationnelle des categories de morphismes partiels avec etablissement systematique des rapports entre ces structures et les classiques structures totales

on the spectrum of cosine functions abstract in this paper we give characterizations of the resolvent set of the generatoraof a strongly continuous cosine functionc t in terms of certain solution properties of the differential equationu t au t f t