open access

https://doi.org/10.14943/83910

https://hdl.handle.net/2115/69568

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

英語

2005

Department of Mathematics, Hokkaido University

Hokkaido University Preprint Series in Mathematics

760

1-22

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.

紀要論文

Version of Record