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Identification of a time-dependent coefficient in a partial differential equation subject to an extra measurement. (English) Zbl 1069.65104
Summary: The problem of recovering a time-dependent coefficient in a parabolic partial differential equation has attracted considerable recent attention. Several finite difference schemes are presented for identifying the function \(u(x,t)\) and the unknown coefficient \(a(t)\) in a one-dimensional partial differential equation. These schemes are developed to determine the unknown properties in a region by measuring only data on the boundary. Our goal has been focused on coefficients that presents physical quantities, for example, the conductivity of a medium. For the convenience of discussion, we will present the results of numerical experiments on several test problems.

MSC:
65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
35R30 Inverse problems for PDEs
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