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An inverse problem for the heat equation

Published online by Cambridge University Press:  14 November 2011

A. G. Ramm
A. G. Ramm
Affiliation:
Mathematics Department, Kansas State University, Manhattan, KS 66506-2602, U.S.A. e-mail: ramm@ ksuvm.ksu.edu
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Synopsis

Uniqueness of the solution to the following inverse problem is established. Given the heat equation, the initial temperature, the boundary regime at the left end of a finite rod and the measurements of the temperature at an intermediate point of the rod, find the temperature at the right end of the rod.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 123 , Issue 6 , 1993 , pp. 973 - 976
Copyright
Copyright © Royal Society of Edinburgh 1993

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References

1Gelfand, I. and Shilov, G.. Generalized functions, vol. I (New York: Academic Press, 1964).Google Scholar
2Ladyzhenskaya, O., Solonnikov, V. and Uraltseva, N.. Linear and Quasilinear Equations of Parabolic Type (Providence, RI: American Mathematical Society, 1968).CrossRefGoogle Scholar
3Saut, J. C. and Scheurer, B.. Unique continuation for some evolution equation. J. Differential Equations 66 (1987), 118–139.CrossRefGoogle Scholar
4Schonbek, T.. On uniqueness for a non-linear heat equation. Math. Comput. Modeling 18 (1993). Special issue Multidimensional Inverse Problems, edited by A. G. Ramm.CrossRefGoogle Scholar