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

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83739

Title: On blow up rate for sign-changing solutions in a convex domain
Authors: Giga, Y. Browse this author
Matsui, S. Browse this author
Sasayama, S. Browse this author
Issue Date: Jul-2003
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 594
Start Page: 1
End Page: 12
Abstract: 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.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69343
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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