On a class of nonlinear anisotropic parabolic problems (Q2799608)
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scientific article; zbMATH DE number 6568398
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a class of nonlinear anisotropic parabolic problems |
scientific article; zbMATH DE number 6568398 |
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On a class of nonlinear anisotropic parabolic problems (English)
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13 April 2016
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anisotropic Sobolev space
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strongly nonlinear parabolic problems
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weak solution
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In this paper the authors study the existence of the solution of the Cauchy-Dirichlet problem NEWLINE\[NEWLINEu_t + Au + g(t,x,u) + \gamma|u|^{p_0-2}u =fNEWLINE\]NEWLINE with \(u_0(x)\) as initial datum and \(u(x,t)\) vanishing on the parabolic boundary. They prove that the solution is in an anisotropic Sobolev spaces if it is assumed that \(f\) belongs to its dual and \(g\) satisfies suitable growth and sign conditions.
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