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.


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