Blow-up behavior for a semilinear heat equation with a nonlinear boundary condition

Sheng Chen Fu; Jong Shenq Guo; Je Chiang Tsai

doi:10.2748/tmj/1113247131

Blow-up behavior for a semilinear heat equation with a nonlinear boundary condition

Sheng Chen Fu
, Jong Shenq Guo
, Je Chiang Tsai

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

15 Citations (Scopus)

Abstract

We study the blow-up behaviors of solutions of a semilinear heat equation with a nonlinear boundary condition. Under certain conditions, we prove that the blow-up point occurs only at the boundary. Then, by applying the well-known method of Giga-Kohn, we derive the time asymptotic of solutions near the blow-up time. Finally, we prove that the blow-up is complete.

Original language	English
Pages (from-to)	565-581
Number of pages	17
Journal	Tohoku Mathematical Journal
Volume	55
Issue number	4
DOIs	https://doi.org/10.2748/tmj/1113247131
Publication status	Published - 2003

ASJC Scopus subject areas

General Mathematics

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10.2748/tmj/1113247131

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title = "Blow-up behavior for a semilinear heat equation with a nonlinear boundary condition",

abstract = "We study the blow-up behaviors of solutions of a semilinear heat equation with a nonlinear boundary condition. Under certain conditions, we prove that the blow-up point occurs only at the boundary. Then, by applying the well-known method of Giga-Kohn, we derive the time asymptotic of solutions near the blow-up time. Finally, we prove that the blow-up is complete.",

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AU - Guo, Jong Shenq

AU - Tsai, Je Chiang

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N2 - We study the blow-up behaviors of solutions of a semilinear heat equation with a nonlinear boundary condition. Under certain conditions, we prove that the blow-up point occurs only at the boundary. Then, by applying the well-known method of Giga-Kohn, we derive the time asymptotic of solutions near the blow-up time. Finally, we prove that the blow-up is complete.

AB - We study the blow-up behaviors of solutions of a semilinear heat equation with a nonlinear boundary condition. Under certain conditions, we prove that the blow-up point occurs only at the boundary. Then, by applying the well-known method of Giga-Kohn, we derive the time asymptotic of solutions near the blow-up time. Finally, we prove that the blow-up is complete.

UR - https://www.scopus.com/pages/publications/1642491911

UR - https://www.scopus.com/pages/publications/1642491911#tab=citedBy

U2 - 10.2748/tmj/1113247131

DO - 10.2748/tmj/1113247131

M3 - Article

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SN - 0040-8735

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EP - 581

JO - Tohoku Mathematical Journal

JF - Tohoku Mathematical Journal

IS - 4

ER -

Blow-up behavior for a semilinear heat equation with a nonlinear boundary condition

Abstract

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