Boundedness of global solutions for a heat equation with exponential gradient source (Q655600)
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scientific article; zbMATH DE number 5994548
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Boundedness of global solutions for a heat equation with exponential gradient source |
scientific article; zbMATH DE number 5994548 |
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Boundedness of global solutions for a heat equation with exponential gradient source (English)
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5 January 2012
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Summary: We consider a one-dimensional semilinear parabolic equation with exponential gradient source and provide a complete classification of large time behavior of the classical solutions: either the space derivative of the solution blows up in finite time with the solution itself remaining bounded, or the solution is global and converges in \(C^1\) norm to the unique steady state. The main difficulty is to prove \(C^1\) boundedness of all global solutions. To do so, we explicitly compute a nontrivial Lyapunov's functional by carrying out the method of Zelenyak.
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one space dimension
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large time behavior
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Lyapunov's functional
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