Uniform blow-up estimates for nonlinear heat equations and applications (Q1852688)
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scientific article; zbMATH DE number 1850438
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Uniform blow-up estimates for nonlinear heat equations and applications |
scientific article; zbMATH DE number 1850438 |
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Uniform blow-up estimates for nonlinear heat equations and applications (English)
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16 September 2003
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In this survey the authors review their results on sharp uniform estimates at blow-up and on the blow-up profiles of solutions of the equation \(u_t=\Delta u + |u|^{p-1}u\) in \(\mathbb R^N\) where \(p>1\) and \((N-2)p<N+2\). Many of these results are obtained using a Liouville theorem for solutions of the above equation that are defined on \(\mathbb R^N\times (-\infty,0)\).
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semilinear parabolic equation
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blow-up profiles
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Liouville theorem
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