Existence of solutions for the evolution \(p(x)\)-Laplacian equation not in divergence form (Q411104)
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scientific article; zbMATH DE number 6021763
| Language | Label | Description | Also known as |
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| English | Existence of solutions for the evolution \(p(x)\)-Laplacian equation not in divergence form |
scientific article; zbMATH DE number 6021763 |
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Existence of solutions for the evolution \(p(x)\)-Laplacian equation not in divergence form (English)
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4 April 2012
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Summary: The existence of weak solutions to the initial Dirichlet problem of the equation \(u_t = u\,\text{div}(|\nabla u|^{p(x)-2}\nabla u)\), with \(\inf p(x) > 2\) is studied. We adopt the method of parabolic regularization. After establishing some necessary uniform estimates on the approximate solutions, we prove the existence of weak solutions.
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