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Blow-up directions at space infinity for solutions of semilinear heat equations
Title: | Blow-up directions at space infinity for solutions of semilinear heat equations |
Authors: | Giga, Yoshikazu Browse this author | Umeda, Noriaki Browse this author |
Issue Date: | 2005 |
Publisher: | Department of Mathematics, Hokkaido University |
Journal Title: | Hokkaido University Preprint Series in Mathematics |
Volume: | 760 |
Start Page: | 1 |
End Page: | 22 |
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. |
Type: | bulletin (article) |
URI: | http://hdl.handle.net/2115/69568 |
Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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