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Determination of an unknown coefficient in a parabolic inverse problem. (English) Zbl 1059.35161

Summary: We study a parabolic inverse problem of finding \(a(t)\) such that \(u_t=a(t)u_{xx}\) subject to initial-boundary value conditions and an over specified condition. We use the over-specified information to solve for the unknown function and then transform these inverse problems into some nonclassical equations in which a trace type of functional is involved. By applying the maximum principle, we deduce some a priori estimates for the solution of our nonclassical problem. Then the continuity method can be applied to establish the global existences of solutions to these problems.

MSC:

35R30 Inverse problems for PDEs
65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
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