Existence and asymptotic behaviour of solutions of a nonlinear evolution problem (Q1978980)
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scientific article; zbMATH DE number 1450134
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Existence and asymptotic behaviour of solutions of a nonlinear evolution problem |
scientific article; zbMATH DE number 1450134 |
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Existence and asymptotic behaviour of solutions of a nonlinear evolution problem (English)
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22 May 2000
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The author proves the existence and investigates the asymptotic behaviour of solutions to the system \[ u'' + Au - \Delta u' + |v|^{\rho + 2}|u|^{\rho}u = f_1,\qquad v'' + Av - \Delta v' + |u|^{\rho + 2} |v|^{\rho}v = f_2, \] where \(A\) denotes the so-called \(p\)-Laplacian operator. The standard Galerkin method is used in combination with energy type estimates to prove existence and decay of global solutions when time tends to infinity.
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\(p\)-Laplacian
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pseudo-Laplacian
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Galerkin method
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energy type estimates
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