An approximation theorem of Runge type for the heat equation
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- by B. Frank Jones PDF
- Proc. Amer. Math. Soc. 52 (1975), 289-292 Request permission
Abstract:
If $\Omega$ is an open subset of ${{\mathbf {R}}^{n + 1}}$, the approximation problem is to decide whether every solution of the heat equation on $\Omega$ can be approximated by solutions defined on all of ${{\mathbf {R}}^{n + 1}}$. The necessary and sufficient condition on $\Omega$ which insures this type of approximation is that every section of $\Omega$ taken by hyperplanes orthogonal to the $t$-axis be an open set without “holes,” i.e., whose complement has no compact component. Part of the proof involves the Tychonoff counterexample for the initial value problem.References
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Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 52 (1975), 289-292
- MSC: Primary 35K05
- DOI: https://doi.org/10.1090/S0002-9939-1975-0387815-9
- MathSciNet review: 0387815