Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 17, pp. 1-9.
Title: Life span of blow-up solutions for higher-order semilinear
parabolic equations
Author: Fuqin Sun (Tianjin Univ. of Technology and Education, China)
Abstract:
In this article, we study the higher-order semilinear parabolic
equation
$$\displaylines{
u_t+(-\Delta)^m u=|u|^p, \quad (t,x)\in
\mathbb{R}^1_+\times \mathbb{R}^N,\cr
u(0,x)= u_0(x),\quad x\in \mathbb{R}^N.
}$$
Using the test function method, we derive the blow-up
critical exponent. And then based on integral inequalities,
we estimate the life span of blow-up solutions.
Submitted August 17, 2009. Published January 27, 2010.
Math Subject Classifications: 35K30, 35K65.
Key Words: Higher-order parabolic equation;
critical exponent; life span; test function method.