Slim Tayachi

Asymptotically self-similar global solutions of a semilinear parabolic equation with a nonlinear gradient term

We study the existence and the asymptotic behaviour of global solutions of the semilinear parabolic equation u(0) = ϧwhere a, b ∈ℝ, q > 1, p > 1. For q = 2p/ ( p +1) and ½ 1(p-1)>1 (equivalently, q > ( n + 2)/( n + 1)), we prove the existence of mild global solutions for small initial data with respect to some norm. Some of those solutions are asymptotically self-similar.

Asymptotically self-similar global solutions of a general semilinear heat equation

Abstract. We consider the general nonlinear heat equation

ASYMPTOTIC SELF-SIMILAR BEHAVIOR OF SOLUTIONS FOR A SEMILINEAR PARABOLIC SYSTEM

\partial_t u = \Delta u +a|u|^{p_1-1}u+g(u), u(0)=\varphi,

The nonlinear heat equation with high order mixed derivatives of the Dirac delta as initial values

on

ASYMPTOTICALLY SELF-SIMILAR GLOBAL SOLUTIONS OF A DAMPED WAVE EQUATION

(0,\infty)\times I\!\!R^n ,

The nonlinear heat equation involving highly singular initial values and new blowup and life span results

where

Optimal condition for non-simultaneous blow-up in a reaction-diffusion system

a\in I\!\!R, p_1>1+(2/n)

Exact self-similar blow-up of solutions of a semilinear parabolic equation with a nonlinear gradient term

and g satisfies certain growth conditions. We prove the existence of global solutions for small initial data with respect to a norm which is related to the structure of the equation. We also prove that some of those global solutions are asymptotic for large time to self-similar solutions of the single power nonlinear heat equation, i.e. with

Global existence, asymptotic behavior and self-similar solutions for a class of semilinear parabolic systems

g\equiv 0.