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Proceedings of the American Mathematical Society

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

 

 

The determination of a parabolic equation from initial and final data


Author: William Rundell
Journal: Proc. Amer. Math. Soc. 99 (1987), 637-642
MSC: Primary 35R30; Secondary 35K05
DOI: https://doi.org/10.1090/S0002-9939-1987-0877031-4
MathSciNet review: 877031
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Abstract: It is shown that an unknown, spatially-dependent coefficient $ a(x)$ in the parabolic equation $ ut - \Delta u + a(x)u = 0$ can be determined from a knowledge of both initial and final data. An existence and uniqueness theorem is given and the continuous dependence of the function $ a(x)$ on the data is examined.


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DOI: https://doi.org/10.1090/S0002-9939-1987-0877031-4
Article copyright: © Copyright 1987 American Mathematical Society