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

Abstract

In this article, we study the higher-order semilinear parabolic equation $$displaylines{ u_t+(-Delta)^m u=|u|^p, quad (t,x)in mathbb{R}^1_+imes mathbb{R}^N,cr u(0,x)= u_0(x),quad xin mathbb{R}^N. }$$ 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.

Keywords

• Higher-order parabolic equation
• critical exponent
• life span
• test function method