On the Cauchy problem for systems -- parabolic systems (Q2756128)
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scientific article; zbMATH DE number 1672562
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Cauchy problem for systems -- parabolic systems |
scientific article; zbMATH DE number 1672562 |
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15 December 2002
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\(p\)-parabolic systems
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higher-order parabolic systems
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well-posedness
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On the Cauchy problem for systems -- parabolic systems (English)
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The paper deals with the theory of the Cauchy problem for parabolic systems. The author shows existence and other properties, under the assumption of \(H^\infty\) well-posedness, for a special class of higher-order parabolic systems: the \(p\)-parabolic systems. Moreover some conditions are given that imply \(H^\infty\) well-posedness. NEWLINENEWLINENEWLINEFinally, a modification of the notion of the \(p\)-parabolic system is given, in such a way that the property is invariant under the similar transformation. The definition of the \(p\)-parabolic system was originally due to \textit{I.~G.~Petrowsky} [Selected works. Part I: Systems of partial differential equations and algebraic geometry, Classics of Soviet Mathematics, Gordon and Breach, Amsterdam (1996; Zbl 0948.01042)].
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