Almost Periodicity of Inhomogeneous Parabolic Evolution Equations

Existence of S-almost Periodic Solutions to a Class of Nonautonomous Stochastic Evolution Equations

The paper studies the notion of Stepanov almost periodicity (or S-almost periodicity) for stochastic processes, which is weaker than the notion of quadratic-mean almost periodicity. Next, we make extensive use of the so-called Acquistapace and Terreni conditions to prove the existence and uniqueness of a Stepanov (quadratic-mean) almost periodic solution to a class of nonautonomous stochastic e...

Parabolic Evolution Equations with Asymptoticallyautonomous

We study retarded parabolic non{autonomous evolution equations whose coeecients converge as t ! 1 such that the autonomous problem in the limit has an exponential dichotomy. Then the non{autonomous problem inherits the exponential dichotomy and the solution of the inhomogeneous equation tends to the stationary solution at innnity. We use a generalized characteristic equation to deduce the expon...

A Quasilinear Parabolic Equation With Inhomogeneous Density and Absorption

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...

A weighted symmetrization for nonlinear elliptic and parabolic equations in inhomogeneous media

In the theory of elliptic equations, the technique of Schwarz symmetrization is one of the tools used to obtain a priori bounds for classical and weak solutions in terms of general information on the data. A basic result says that, in the absence of the zero-order term, the symmetric rearrangement of the solution u of an elliptic equation, that we write u∗, can be compared pointwise with the so...