The determination of a parabolic equation from initial and final data

Rundell, William

doi:10.1090/S0002-9939-1987-0877031-4

The determination of a parabolic equation from initial and final data
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Proc. Amer. Math. Soc. 99 (1987), 637-642 Request permission

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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The determination of a coefficient in a parabolic differential equation from overspecified boundary data

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