Nonuniqueness of the positive Dirichlet problem for parabolic equations in cylinders (Q1908181)
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scientific article; zbMATH DE number 847487
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Nonuniqueness of the positive Dirichlet problem for parabolic equations in cylinders |
scientific article; zbMATH DE number 847487 |
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Nonuniqueness of the positive Dirichlet problem for parabolic equations in cylinders (English)
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1996
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This interesting paper investigates uniqueness of nonnegative solutions to parabolic equations (heat equations) in cylinders of \(\mathbb{R}^{n+ 1}\) with zero Dirichlet boundary conditions, when the bases of the cylinders are unbounded. There are given necessary and sufficient conditions for the uniqueness in terms of geometric properties of the bases. Several examples concerning the uniqueness of nonnegative solutions are also given.
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necessary and sufficient conditions for uniqueness
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