Electron. J. Diff. Equ., Vol. 2010(2010), No. 17, pp. 1-9.

Life span of blow-up solutions for higher-order semilinear parabolic equations

Fuqin Sun

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.

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Fuqin Sun
School of Science
Tianjin University of Technology and Education
Tianjin 300222, China
email: sfqwell@163.com

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