Monotonicity of solutions and blow-up for semilinear parabolic equations with nonlinear memory (Q1880224)
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scientific article; zbMATH DE number 2101585
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Monotonicity of solutions and blow-up for semilinear parabolic equations with nonlinear memory |
scientific article; zbMATH DE number 2101585 |
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Monotonicity of solutions and blow-up for semilinear parabolic equations with nonlinear memory (English)
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22 September 2004
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The author considers the nonlocal semilinear parabolic equation \[ u_t-\Delta u =\int_0^t u^p(x,t)\,ds, \quad x\in \Omega, t>0, \] under homogeneous Dirichlet boundary condition. For solutions that are monotone in time the blow-up rate is known to be the same as for the ODE \(u_t=u^p\). The author proves the existence of the monotone solutions.
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nonlocal parabolic equation
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nonlinear memory
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blow-up rate
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monotonicity
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