Admissible and regular potentials for positive \(C_ 0\)-semigroups and application to heat semigroups (Q1313480)
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scientific article; zbMATH DE number 492609
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Admissible and regular potentials for positive \(C_ 0\)-semigroups and application to heat semigroups |
scientific article; zbMATH DE number 492609 |
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Admissible and regular potentials for positive \(C_ 0\)-semigroups and application to heat semigroups (English)
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31 January 1994
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The author solves the following initial value problem given by the heat equation by using the semi-group theory \[ u_ t= {\textstyle {1\over 2}} \Delta u- V_ u, \qquad u(0)= u_ 0. \] The main tool in the investigation is the Voigt's perturbation theory of positive \(C_ 0\)- semigroups in \(L^ p\) spaces where \(1\leq p<\infty\).
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initial value problem
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heat equation
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semi-group theory
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Voigt's perturbation theory of positive \(C_ 0\)-semigroups in \(L^ p\) spaces
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