Abstract quasilinear parabolic equations (Q798863)
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scientific article; zbMATH DE number 3871894
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Abstract quasilinear parabolic equations |
scientific article; zbMATH DE number 3871894 |
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Abstract quasilinear parabolic equations (English)
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1984
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The author deals with an abstract quasilinear parabolic problem \(u'(t)=A(t,u(t))u(t)+f(t,u(t)), t>0\), \(u(0)=u_ 0\) in a Banach space X. His theorems on existence and uniqueness are such that a concrete quasilinear parabolic problem can be attacked without imposing growth conditions on the coefficients. Regularity results are obtained by means of interpolation spaces based on infinitesimal generators of bounded semi-groups. The characterization of those spaces in classical analytical terms are given.
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abstract quasilinear parabolic problem
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existence
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uniqueness
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Regularity
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interpolation spaces
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infinitesimal generators
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bounded semi- groups
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