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

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83910

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
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

Submitter: 数学紀要登録作業用

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