THE QUENCHING BEHAVIOR OF A SEMILINEAR HEAT EQUATION WITH A SINGULAR BOUNDARY OUTFLUX

被引：2

作者：

Selcuk, Burhan ^{[1
]}

Ozalp, Nuri ^{[2
]}

机构：

[1] Karabuk Univ, Dept Comp Engn, TR-78050 Baliklarkayasi Mevkii, Turkey

[2] Ankara Univ, Dept Math, TR-06100 Besevler, Turkey

来源：

QUARTERLY OF APPLIED MATHEMATICS | 2014年 / 72卷 / 04期

关键词：

Semilinear heat equation; singular boundary outflux; quenching; quenching point; quenching time; maximum principles; PARABOLIC PROBLEMS;

D O I：

10.1090/S0033-569X-2014-01367-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the quenching behavior of the solution of a semilinear heat equation with a singular boundary outflux. We prove a finite-time quenching for the solution. Further, we show that quenching occurs on the boundary under certain conditions and we show that the time derivative blows up at a quenching point. Finally, we get a quenching rate and a lower bound for the quenching time.

引用

页码：747 / 752

页数：6

共 19 条

[1]

Chan C. Y., 1992, WORLD C NONL AN 92 T, VI-IV, P427

[2]

Chan C.Y., 1996, P DYNAMIC SYSTEMS AP, V2, P107

[3] Quenching for a degenerate parabolic problem due to a concentrated nonlinear source [J].

Chan, CY ;

Jiang, XO .

QUARTERLY OF APPLIED MATHEMATICS, 2004, 62 (03) :553-568

[4] Parabolic problems with nonlinear absorptions and releases at the boundaries [J].

Chan, CY ;

Yuen, SI .

APPLIED MATHEMATICS AND COMPUTATION, 2001, 121 (2-3) :203-209

[5]

CHAN CY, 1995, WORLD SCI SER APPL A, V4

[6] Quenching for a nonlinear diffusion equation with a singular boundary condition [J].

Deng, K ;

Xu, MX .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 1999, 50 (04) :574-584

[7]

DENG K, 2003, COMM APPL ANAL, V7

[8] Existence, uniqueness, and quenching properties of solutions for degenerate semilinear parabolic problems with second boundary conditions [J].

Dyakevich, Nadejda E. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 338 (02) :892-901

[9] QUENCHING ON THE BOUNDARY [J].

FILA, M ;

LEVINE, HA .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1993, 21 (10) :795-802

[10] Blow-up behavior for a semilinear heat equation with a nonlinear boundary condition [J].

Fu, SC ;

Guo, JS ;

Tsai, JC .

TOHOKU MATHEMATICAL JOURNAL, 2003, 55 (04) :565-581

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