Mathematica Bohemica, Vol. 144, No. 3, pp. 287-297, 2019
Total blow-up of a quasilinear heat equation with slow-diffusion for non-decaying initial data
Amy Poh Ai Ling, Masahiko Shimojō
Received February 25, 2018. Published online October 22, 2018.
Abstract: We consider solutions of quasilinear equations $u_t=\Delta u^m + u^p$ in $\R^N$ with the initial data $u_0$ satisfying $ 0 < u_0< M$ and $\lim_{|x|\to\infty}u_0(x)=M$ for some constant $M>0$. It is known that if $0<m <p$ with $p>1$, the blow-up set is empty. We find solutions $u$ that blow up throughout $\R^N$ when $m>p>1$.
Keywords: quasilinear heat equation; total blow-up; blow-up only at space infinity
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Affiliations: Amy Poh Ai Ling (corresponding author), Department of Mathematics, Faculty of Science, Okayama University, 3-1-1 Tsushimanaka, Kitaku, Okayama City, 700-8530, Japan, and Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, 4-21-1 Nakano, Nakano Ward, Tokyo City, 164-8525, Japan, e-mail: amypoh.al@okayama-u.ac.jp; Masahiko Shimojō, Department of Applied Mathematics, Faculty of Science, Okayama University of Science, 1-1 Ridaicho, Kita Ward, Okayama City, 700-0005, Japan, e-mail: shimojo@xmath.ous.ac.jp
