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Numerical solutions of some parabolic inverse problems
Author(s) -
Can John R.,
Yin HongMing
Publication year - 1990
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690060207
Subject(s) - mathematics , parabolic partial differential equation , galerkin method , mathematical analysis , inverse problem , inverse , boundary value problem , trace (psycholinguistics) , boundary (topology) , function (biology) , type (biology) , partial differential equation , finite element method , geometry , linguistics , philosophy , physics , evolutionary biology , biology , thermodynamics , ecology
In this article we transform a large class of parabolic inverse problems into a nonclassical parabolic equation whose coefficients consist of trace type functionals of the solution and its derivatives subject to some initial and boundary conditions. For this nonclassical problem, we introduce a variational form by defining a new function. Both continuous and discrete Galerkin procedures are illustrated in this paper. The error estimates are also derived.