QUENCHING FOR A REACTION-DIFFUSION EQUATION WITH WEAK SINGULARITIES

This paper studies the following reaction-diffusion equation with a weak singular boundary condition. The primary objective for this problem is to analyze the quenching properties. It is obtained that finite time quenching occurs on the left boundary, the time derivative of the solution blows up at...

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Bibliographic Details
Published inTWMS journal of applied and engineering mathematics Vol. 12; no. 4; p. 1160
Main Author Selcuk, B
Format Journal Article
LanguageEnglish
Published Istanbul Turkic World Mathematical Society 01.09.2022
Elman Hasanoglu
Subjects
Boundary conditions
Boundary value problems
Differential equations, Partial
Mathematical research
Reaction-diffusion equations
Singularities (Mathematics)
Turkey
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Summary:This paper studies the following reaction-diffusion equation with a weak singular boundary condition. The primary objective for this problem is to analyze the quenching properties. It is obtained that finite time quenching occurs on the left boundary, the time derivative of the solution blows up at the same time and also quenching rate estimates of the solution of the eqaution [k.sub.t](x,t) = [k.sub.xx](x,t) + ln [alpha]k(x,t), (x,t) [member of] (0,1) X (0,T) with [k.sub.x] (0,t) = - ln[beta]k(0,t), [k.sub.x] (1, t) =0, t [member of] (0,T) and initial function k (x, 0) = [k.sub.0] (x) with [0,1] [right arrow] (0,1) where 0 < [alpha], [beta] < 1 and T is a finite time. Keywords: Reaction-diffusion equation, Singular boundary condition, Quenching, Maximum principles. AMS Subject Classification: 35K55, 35K67, 35B50.
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ISSN:2146-1147
2146-1147