Dept. Math, Hokkaido Univ. EPrints Server

Blow-up directions at space infinity for solutions of semilinear heat equations

Preprint Series # 760
Giga, Yoshikazu and Umeda, Noriaki Blow-up directions at space infinity for solutions of semilinear heat equations. (2005);

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Abstract

A blowing up solution of the semilinear heat equation $u_t =\Delta u+f(u) $ with $f$ satisfying $\liminf f(u)/u^p >0$ for some $p>1$ is considered when initial data $u_0 $ satisfies $u_0 \le M$, $u_0 \not\equiv M$ and $\lim_{m\to \infty } $ $ \inf_{x\in B_m } u_0 (x) =M$ with sequence of ball $\{ B_m \} $ whose radius diverging to infinity. It is shown that the solution blows up only at space infinity. A notion of blow-up direction is introduced. A characterization for blow-up direction is also established.

Item Type:Preprint
Subjects:35-xx PARTIAL DIFFERENTIAL EQUATIONS
ID Code:1249