Global existence for a semilinear parabolic Volterra equation (Q2644902)
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| Language | Label | Description | Also known as |
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| English | Global existence for a semilinear parabolic Volterra equation |
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Global existence for a semilinear parabolic Volterra equation (English)
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1992
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We prove wellposedness in the large for a semilinear parabolic Volterra equation in spaces of integrable functions. The nonlinearity is assumed to be nonincreasing in u and to be of at most quadratic growth in \(\nabla u\). The proof relies on maximal regularity of the linearized equation and on the maximum principle.
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strong solutions
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maximal regularity
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maximum principle
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continuation method
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accretive operators
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heat conduction in materials with memory
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semilinear parabolic Volterra equation
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