A GRADIENT-LIKE NONAUTONOMOUS EVOLUTION PROCESS

A Gradient-like nonautonomous Evolution Process

Tomás Caraballo* Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla Spain E-mail: [email protected] Alexandre N. Carvalho† Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo-Campus de São Carlos, Caixa Postal 668, 13560-970 São Carlos SP, Brazil. E-mail: [email protected] José A. Langa‡ Departament...

Asymptotic Behaviour of Parabolic Nonautonomous Evolution Equations

Evolution Semigroups for Nonautonomous Cauchy Problems

In this paper, we characterize wellposedness of nonautonomous, linear Cauchy problems (NCP ) { u̇(t) = A(t)u(t) u(s) = x ∈ X on a Banach space X by the existence of certain evolution semigroups. Then, we use these generation results for evolution semigroups to derive wellposedness for nonautonomous Cauchy problems under some “concrete” conditions. As a typical example, we discuss the so called “...

Existence of Stepanov-like Square-mean Pseudo Almost Automorphic Solutions to Nonautonomous Stochastic Functional Evolution Equations

We introduce the concept of bi-square-mean almost automorphic functions and Stepanov-like square-mean pseudo almost automorphic functions for stochastic processes. Using the results, we also study the existence and uniqueness theorems for Stepanov-like square-mean pseudo almost automorphic mild solutions to a class of nonautonomous stochastic functional evolution equations in a real separable H...

Maximal regularity for nonautonomous evolution equations

We derive sufficient conditions, perturbation theorems in particular, for nonautonomous evolution equations to possess the property of maximal Lp regularity. 1991 Mathematics Subject Classification. 35K90, 47D06.