The global existence of nonlinear evolutionary equation with small delay (Q1760611)
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scientific article; zbMATH DE number 6106154
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The global existence of nonlinear evolutionary equation with small delay |
scientific article; zbMATH DE number 6106154 |
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The global existence of nonlinear evolutionary equation with small delay (English)
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15 November 2012
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Summary: We investigate the global existence of the delayed nonlinear evolutionary equation \(\partial_t u + Au = f(u(t), u(t - \tau))\) . Our work space is the fractional powers space \(X^a\). Under the fundamental theorem on sectorial operators, we make use of the fixed-point principle to prove the local existence and uniqueness theorem. Then, the global existence is obtained by Gronwall's inequality.
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delayed nonlinear evolutionary equation
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fractional powers space
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Gronwall's inequality
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0.813019335269928
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0.8079943656921387
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0.7932571768760681
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