Boundedness of global solutions of nonlinear diffusion equations (Q1196635)
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scientific article; zbMATH DE number 89288
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Boundedness of global solutions of nonlinear diffusion equations |
scientific article; zbMATH DE number 89288 |
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Boundedness of global solutions of nonlinear diffusion equations (English)
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16 January 1993
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This paper deals with large time behaviour of solutions of Dirichlet- initial value problems for the equation \(u_ t=\Delta(| u|^{m- 1}u)+f(u)\) when \(f\) grows superlinearly. In particular the question of global existence without uniform a priori bounds is examined. The case when \(m=1\) and \(f\) is allowed to grow exponentially is of particular concern and it is shown that global existence without uniform bounds is impossible in one and two dimensions.
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blow-up
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large time behaviour
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Dirichlet-initial value problems
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global existence
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