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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

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