On the steady states of a nonlocal semilinear heat equation (Q2724362)
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scientific article; zbMATH DE number 1616222
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the steady states of a nonlocal semilinear heat equation |
scientific article; zbMATH DE number 1616222 |
Statements
2 July 2002
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existence and nonexistence of steady states
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nonlocal boundary value problems
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On the steady states of a nonlocal semilinear heat equation (English)
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The paper deals with existence and nonexistence of steady states for the following nonlocal semilinear heat equation NEWLINE\[NEWLINE u_t= u_{xx} + \varepsilon \Biggl(\int_0^1 |u(t,x)|dx\Biggr)^q \Biggl/ (1-u)^\betaNEWLINE\]NEWLINE for \(0<x<1\), \(t>0\), with the zero Dirichelet boundary condition and initial condition \(u(x,0)=u_0(x)\). By using the strong maximum principle and modifying a technique introduced by \textit{K. Deng} [SIAM J. Math. Anal. 26, 98-111 (1995; Zbl 0824.35010)], the authors obtain existence and nonexistence results of steady states, related to the value of the parameter \(\varepsilon>0\).
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