On blow up rate for sign-changing solutions in a convex domain

Giga, Y.; Matsui, S.; Sasayama, S.

Hokkaido University Preprint Series in Mathematics, 2003, 594, 1-12

Permalink : https://doi.org/10.14943/83739

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アクセス権	open access
DOI	https://doi.org/10.14943/83739
URI	https://hdl.handle.net/2115/69343
タイトル	On blow up rate for sign-changing solutions in a convex domain
著者	Giga, Y. ; Matsui, S. ; Sasayama, S.
著者名 Giga, Y.
著者名 Matsui, S.
著者名 Sasayama, S.
言語	英語
発行日	2003-07
出版者	Department of Mathematics, Hokkaido University
収録物名	Hokkaido University Preprint Series in Mathematics
巻(号)	594
ページ	1-12
抄録	This paper studies a growth rate of a solution blowing up at time T of the semilinear heat equation Ut - £:iu - lulP-1u = 0 in a convex domain D in Rn with zero-boundary condition. For a subcritical p E (1, (n + 2)/(n - 2)) a growth rate estimate lu(x, t)I :S C(T- t)-1/(p-l), x E D, t E (0, T) is established with C independent oft provided that D is uniformly 02. The estimate applies to sign-changing solutions. The same estimate has been recently established when D = Rn by authors. The proof is similar but we need to establish Lh - Lk estimate for a time-dependent domain because of the presence of the boundary.
資源タイプ	紀要論文
出版タイプ	Version of Record