# 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);

 TeX DVI81Kb

## 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 35-xx PARTIAL DIFFERENTIAL EQUATIONS 1249