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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
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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Article copyright: © Copyright 1987 American Mathematical Society