existence results for initial value problems for neutral functional differential equations abstract existence results for initial value problems for neutral functional differential equations are given the results are based on the leray schauder alternative and rely on a priori bounds on solutions applications to certain integro differential equations are also given

asymptotically almost periodic solutions for abstract neutral integro differential equations we study the existence of asymptotically almost periodic classical solutions for a class of abstract neutral integro differential equation with unbounded delay a concrete application to partial neutral integro differential equations which arise in the study of heat conduction in fading memory material is considered

corner singularities and boundary layers in a simple convection diffusion problem abstract a singularly perturbed convection diffusion problem posed on the unit square is considered its solution may have exponential and parabolic boundary layers and corner singularities may also be present pointwise bounds on the solution and its derivatives are derived the dependence of these bounds on the small diffusion coefficient on the regularity of the data and on the compatibility of the data at the corners of the domain are all made explicit the bounds are derived by decomposing the solution into a sum of solutions of elliptic boundary value problems posed on half planes then analyzing these simpler problems

an open system approach for the characterization of spatio temporal chaos we investigate the structure of the invariant measure of space time chaos by adopting an open system point of view we consider large but finite windows of formally infinite one dimensional lattices and quantify the effect of the interaction with the outer region by mapping the problem on the dynamical characterization of localized perturbations this latter task is performed by suitably generalizing the concept of lyapunov spectrum to cope with perturbations that propagate outside the region under investigation as a result we are able to introduce a volume propagation velocity i e the velocity with which ensembles of localized perturbations tend to fill volumes in the neighbouring regions

existence of solutions of abstract nonlinear second order neutral functional integrodifferential equations abstract sufficient conditions for existence of mild solutions for abstract second order neutral functional integrodifferential equations are established by using the theory of strongly continuous cosine families of operators and the schaefer theorem

existence of solutions for impulsive partial neutral functional differential equations this paper is concerned with partial neutral functional differential equations of first and second order with impulses we establish some results of existence of mild solutions for these classes of equations

pointwise a posteriori error estimates for elliptic problems on highly graded meshes pointwise a posteriori error estimates are derived for linear second order elliptic problems over general polygonal domains in 2d the analysis carries over regardless of convexity accounting even for slit domains and applies to highly graded unstructured meshes as well a key ingredient is a new asymptotic a priori estimate for regularized green s functions the estimators lead always to upper bounds for the error in the maximum norm along with lower bounds under very mild regularity and nondegeneracy assumptions the effect of both point and line singularities is examined three popular local estimators for the energy norm are shown to be equivalent when suitably interpreted to those introduced here

entropy of coupled map lattices the entropy of coupled map lattices with respect to the group of space time translations is considered we use the notion of generalized lyapunov spectra to prove the analogue of the ruelle inequality and the pesin formula

maximum norm a posteriori error estimate for a 2d singularly perturbed semilinear reaction diffusion problem a singularly perturbed semilinear reaction diffusion equation posed in the unit square is discretized on arbitrary nonuniform tensor product meshes we establish a second order maximum norm a posteriori error estimate that holds true uniformly in the small diffusion parameter no mesh aspect ratio assumption is made numerical results are presented that support our theoretical estimate

on existence results and qualitative properties of mild solution of semilinear mixed volterra fredholm functional integrodifferential equations in banach spaces in this paper we prove the existence results uniqueness continuous dependence on initial functions and on parameters of mild solution of semilinear mixed volterra fredholm functional integrodifferential equations in banach spaces the closeness and continuous dependence of the mild solution on the right hand side of the equation is also established our analysis is based on the theory of strongly continuous semigroup the nonlinear alternative of leray schauder and the integral inequality established by pachpatte an example is given to illustrate the results

integral inequalities and mild solutions of semilinear neutral evolution equations abstract existence of mild solutions to semilinear neutral evolution equations with nonlocal conditions is proved the result is obtained by using fractional power of operators krasnoselski schaefer type fixed point theorem and by applying a modification of the bihari type inequality to the case of singular integral inequality an application to partial differential equations is given

existence of periodic solutions of partial neutral functional differential equations with unbounded delay abstract in this article we establish a result of existence of periodic solutions for the class of quasi linear partial neutral functional differential equations with unbounded delay that can be described as the abstract functional differential equation d dt x t f t x t ax t g t x t where a is the infinitesimal generator of a strongly continuous semigroup of linear operators on a banach space and f and g are appropriate functions defined on a phase space

existence of solutions of nonlinear abstract neutral integrodifferential equations in this paper we establish a set of sufficient conditions for the existence of mildsolutions of nonlinear neutral integrodifferential equations in banach spaces by using the schaefer fixed point theorem an application is provided to illustrate the theory

nonlocal cauchy problem for analytic resolvent integrodifferential equations in banach spaces abstract in this paper we prove the existence of semi classical and mild solutions of nonlinear integrodifferential equations with nonlocal conditions in banach spaces the results are obtained by using the theory of analytic resolvents and schaefer s fixed point theorem

controllability of neutral functional integrodifferential systems in banach spaces abstract sufficient conditions for controllability of neutral functional integrodifferential systems in a banach space are established the results are obtained by using the schaefer fixed point theorem an example is provided to illustrate the theory

existence of solutions of nonlinear neutral integrodifferential equations in banach spaces abstract in this paper we prove the existence of mild solutions of a nonlinear neutral integrodifferential equation in a banach space the results are obtained by using the schaefer fixed point theorem as an application the controllability problem for the neutral system is discussed

uniform a priori estimates for singularly perturbed elliptic equations in multidimensions we consider a linear singularly perturbed elliptic equation on a bounded domain in mbox smallbbb r n this equation serves as a model for the interplay between the transport term and a relatively small viscosity term in some problems of mathematical physics we establish a priori estimates that hold uniformly in the small parameter from this one can prove an abstract a priori error estimate for the discretization with conforming finite elements for globally directed transport fields we establish a new type of anisotropic a priori estimate for the solution in the case of omega 0 1 2 we prove a priori estimates for certain higher order derivatives in isotropic as well as anisotropic norms in a subsequent paper we will apply these results to show uniform convergence of an exponentially fitted method on rectangular grids

greenʼs function estimates for a singularly perturbed convection diffusion problem we consider a singularly perturbed convection diusion problem posed in the unit square with a horizontal convective direction its solutions exhibit parabolic and exponential boundary layers sharp estimates of the green s function and its first and second order derivatives are derived in the l1 norm the dependence of these estimates on the small diusion parameter is shown explicitly the obtained estimates will be used in a forthcoming numerical analysis of the considered problem

holder estimates for green s functions on convex polyhedral domains and their applications to finite element methods a model second order elliptic equation on a general convex polyhedral domain in three dimensions is considered the aim of this paper is twofold first sharp holder estimates for the corresponding green s function are obtained as an applications of these estimates to finite element methods we show the best approximation property of the error in w 1 infty in contrast to previously known results w p 2 regularity for p 3 which does not hold for general convex polyhedral domains is not required furthermore the new green s function estimates allow us to obtain localized error estimates at a point

on cα holder classical solutions for non autonomous neutral differential equations the nonlinear case abstract in this paper we continue our developments in 19 on the existence of classical solutions for abstract neutral differential equations in the current work we extend the results in 19 for nonlinear neutral differential equations some applications involving nonlinear partial neutral differential equations are presented

on solutions of neutral nonlocal evolution equations with nondense domain in this paper with sadovskii s and banach s fixed point theorems applied we establish some results on the existence of integral solutions strong solutions and strict solutions for a class of nondensely defined neutral evolution equations with nonlocal conditions also an example is given in the end to show the applications of the obtained results

extensive properties of the complex ginzburg landau equation we study the set of solutions of the complex ginzburg landau equation in r d d 3 we consider the global attracting set i e the forward map of the set of bounded initial data and restrict it to a cube q l of side l we cover this set by a minimal number n q l of balls of radius in l infin q l we show that the kolmogorov entropy per unit length exists in particular we bound by which shows that the attracting set is smaller than the set of bounded analytic functions in a strip we finally give a positive lower bound

existence results for partial neutral functional differential equations with unbounded delay abstract we prove the existence of mild solutions for a partial neutral functional integrodifferential equation with unbounded delay using the leray schauder alternative

chronotopic lyapunov analysis i a detailed characterization of 1d systems instabilities in 1d spatially extended systems are studied with the aid of both temporal and spatial lyapunov exponents a suitable representation of the spectra allows a compact description of all the possible disturbances in tangent space the analysis is carried out for chaotic and periodic spatiotemporal patterns singularities of the spectra and localization properties of the associated lyapunov vectors are discussed