Extinction and positivity of solutions of the \(p\)-Laplacian evolution equation on networks (Q643559)
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scientific article; zbMATH DE number 5966284
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Extinction and positivity of solutions of the \(p\)-Laplacian evolution equation on networks |
scientific article; zbMATH DE number 5966284 |
Statements
Extinction and positivity of solutions of the \(p\)-Laplacian evolution equation on networks (English)
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2 November 2011
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An space discrete evolution \(p\)-Laplacian equation is considered. Using vector calculus in networks and a comparison principle, large time behavior of nontrivial solutions is studied. Assuming nonnegative initial data and zero boundary data, it is proved that the solution becomes extinct for \(1<p<2\) and remains positive for \(p\geq 2\).
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discrete \(p\)-Laplacian
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vector calculus on networks
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extinction of solutions
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nonnegative initial data
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zero boundary data
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