Reaction-diffusion problems with singular absorption (Q2768762)
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scientific article; zbMATH DE number 1700117
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Reaction-diffusion problems with singular absorption |
scientific article; zbMATH DE number 1700117 |
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3 February 2002
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spatial-time localization
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stationary problem
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Reaction-diffusion problems with singular absorption (English)
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This article deals with the initial boundary value problem \(u_{t}=u_{xx}-u^{-\beta}\chi(u)\), \(u(x,0)=1,\;-a<x<a\), \(u(-a,t)=u(a,t)=1, t>0\), where \(0<\beta<1\), \(\chi(u)=\begin{cases} 0,& u<0\\ 1,& u\geq 0 \end{cases}\). The authors study the problem of spatial-time localization of a solution of the stationary problem \(u_{xx}=u^{-\beta}\chi(u)\), \(-a<x<a\), \(u(-a)=u(a)=1\).
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