Further study on a nonlinear heat equation (Q5929064)
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scientific article; zbMATH DE number 1588073
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Further study on a nonlinear heat equation |
scientific article; zbMATH DE number 1588073 |
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Further study on a nonlinear heat equation (English)
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3 December 2001
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semilinear parabolic equation
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stability of steady states
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blow-up
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0.93390286
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0.92085785
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0.9154712
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0.9090341
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Large-time behavior of solutions of the equation NEWLINE\[NEWLINEu_t=\Delta u + u^p, \qquad x\in\mathbb{R}^n,NEWLINE\]NEWLINE is studied. It is shown that if \(p>1+2/n\) then the steady state \(v\equiv 0\) is weakly asymptotically stable in a scale of weighted \(L^\infty\)-norms and unstable if the weight is too heavy or too light. The same is true for positive radial steady states when \(n>10\) and \(p\) exceeds a certain critical value. New sufficient conditions on initial-values for decay and blow-up of solutions are also given.
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