Almost Periodicity and Degenerate Parabolic Equations

Almost Periodicity of Inhomogeneous Parabolic Evolution Equations

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 (...

On Degenerate Parabolic Equations

Mohammed Kbiri Alaoui Department of Mathematics, King Khalid University, P.O. Box 9004, Abha, Saudi Arabia Correspondence should be addressed to Mohammed Kbiri Alaoui, mka [email protected] Received 31 March 2011; Accepted 28 July 2011 Academic Editor: Mihai Putinar Copyright q 2011 Mohammed Kbiri Alaoui. This is an open access article distributed under the Creative Commons Attribution License, which...

Periodicity and Almost-periodicity

A note on critical point and blow-up rates for singular and degenerate parabolic equations

In this paper, we consider singular and degenerate parabolic equations$$u_t =(x^alpha u_x)_x +u^m (x_0,t)v^{n} (x_0,t),quadv_t =(x^beta v_x)_x +u^q (x_0,t)v^{p} (x_0,t),$$ in $(0,a)times (0,T)$, subject to nullDirichlet boundary conditions, where $m,n, p,qge 0$, $alpha, betain [0,2)$ and $x_0in (0,a)$. The optimal classification of non-simultaneous and simultaneous blow-up solutions is determin...