Schwarz reflection principles for solutions of parabolic equations
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- by David Colton PDF
- Proc. Amer. Math. Soc. 82 (1981), 87-94 Request permission
Abstract:
A reflection principle is obtained for solutions of the heat equation defined in a cylindrical domain of the form $\Omega \times (0,T)$ where $\Omega$ is a ball in ${{\mathbf {R}}^n}$ and the solution vanishes on $\partial \Omega \times (0,T)$. It is shown that the domain of dependence of the solution at a point outside the cylinder $\Omega \times (0,T)$ is a line segment contained inside $\Omega \times (0,T)$. In the case $n = 2$ this result is generalized to the case of analytic solutions of parabolic equations with analytic coefficients defined in an arbitrary bounded simply connected cylinder $D \times (0,T)$ where the solution vanishes on a portion of $\partial D \times (0,T)$.References
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Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 82 (1981), 87-94
- MSC: Primary 35B60; Secondary 35K10
- DOI: https://doi.org/10.1090/S0002-9939-1981-0603607-X
- MathSciNet review: 603607