Einige Bemerkungen zur Anfangs-Randwertaufgabe \(\partial u/\partial t- h(x,t)\Delta u=f\) mit meßbaren Koeffizienten (Q1059782)
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scientific article; zbMATH DE number 3905085
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Einige Bemerkungen zur Anfangs-Randwertaufgabe \(\partial u/\partial t- h(x,t)\Delta u=f\) mit meßbaren Koeffizienten |
scientific article; zbMATH DE number 3905085 |
Statements
Einige Bemerkungen zur Anfangs-Randwertaufgabe \(\partial u/\partial t- h(x,t)\Delta u=f\) mit meßbaren Koeffizienten (English)
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1984
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From the author's abstract. The mixed problem \(\partial u/\partial t- h(x,t)\Delta u=f\) with measurable coefficient is considered at first for special domains (cubes) by a modification of Banach's fixed point theorem. Starting from this we get an existence and uniqueness theorem for domains of the class \(O^ 2\). - An existence theorem for the heat equation in n dimensions with measurable coefficients on domains with boundary of the class \(C^ 2\) was proved by \textit{S. Campanato} [see Rend. Semin. Mat. Univ. Padova 41(1968), 153-163 (1969; Zbl 0202.376)].
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continuous dependence on the data
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mixed problem
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measurable coefficient
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Banach's fixed point theorem
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existence
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uniqueness
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