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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A Runge theorem for solutions of the heat equation


Author: R. Diaz
Journal: Proc. Amer. Math. Soc. 80 (1980), 643-646
MSC: Primary 35K05; Secondary 31B35, 35E20
DOI: https://doi.org/10.1090/S0002-9939-1980-0587944-2
MathSciNet review: 587944
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Abstract: Let $ {\Omega _1}$ and $ {\Omega _2}$ be open sets in $ {R^n}$ such that $ {\Omega _1} \subset {\Omega _2}$. Every solution of the heat equation on $ {\Omega _1}$ admits approximation on the compact subsets of $ {\Omega _1}$ by functions which satisfy the heat equation throughout $ {\Omega _2}$ if and only if this topological condition is met: For every hyperplane $ \pi $ in $ {R^n}$ orthogonal to the time axis, every compact component of $ \pi \backslash {\Omega _1}$ contains a compact component of $ \pi \backslash {\Omega _2}$.


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DOI: https://doi.org/10.1090/S0002-9939-1980-0587944-2
Keywords: Relative P-Runge domains, parabolic operators, H-Runge pairs, nonuniqueness for the initial value problem
Article copyright: © Copyright 1980 American Mathematical Society