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.