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Determination of an unknown function in a parabolic equation with an overspecified condition
Author(s) -
Chadam John M.,
Yin HongMing
Publication year - 1990
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670130506
Subject(s) - mathematics , parabolic partial differential equation , boundary value problem , mathematical analysis , inverse problem , initial value problem , fixed point theorem , inverse , function (biology) , transformation (genetics) , variable (mathematics) , partial differential equation , geometry , biochemistry , chemistry , evolutionary biology , gene , biology
In this paper we consider the inverse problems of identifying some space‐dependent unknown coefficients in parabolic equations subject to initial boundary value conditions along with an overspecified condition at the final time t = T . We use the overspecified information to transform the problems into non‐linear parabolic equations involving a functional of the solution with respect to the time variable. This transformation allows us to establish existence theorems for these inverse problems by employing the Schauder fixed‐point theorem.