On boundedness, periodicity, and almost periodicity of solutions of some nonlinear parabolic equations

Almost Periodicity of Inhomogeneous Parabolic Evolution Equations

Almost Periodicity, Equi-continuity and Total Boundedness

Let X be a uniform space; that is to say, let X be a space provided with a system of indexed neighborhoods Ua(x) (x(EX, a=index), subject to the conditions (A. Weil) : (1) If xÇzX and if a is an index, then xÇzUa(x)\ (2) If a and /? are indices, then there exists an index y such that xÇzX implies U7(x)ÇZUa(x)r\Up(x); (3) If a is an index, then there exists an index /? such that x, y, zÇzX with ...

Periodicity and Almost-periodicity

Almost-sure Explosive Solutions of Some Nonlinear Parabolic Itô Equations

The paper is concerned with the problem of explosive solutions to a class of nonlinear parabolic Itô equations. Under some sufficient conditions on the initial state and the nonlinear coefficients, it will be shown that the solutions will explode in finite time almost surely. Theorem 3.1 is concerned with the existence of a unique local strong solution. The main result is presented in Theorem 3...

Asymptotic Almost Periodicity of Scalar Parabolic Equations with Almost Periodic Time Dependence

1 1. Introduction This paper is devoted to the study of asymptotic almost periodicity of bounded solutions for the following time almost periodic one dimensional scalar parabolic equation:    u t = u xx + f (t, x, u, u x), t > 0, 0 < x < 1, u(t, 0) = u(t, 1) = 0, t > 0, (1.1) where f : IR 1 × [0, 1] × IR 1 × IR 1 → IR 1 is a C 2 function, and f (t, x, u, p) with all its partial derivatives (...