Inverse problem for the nonlinear heat equation with the final overdetermination. (English) Zbl 0835.35157

Summary: An inverse problem for the one-dimensional heat equation with a nonlinear term and an unknown space-dependent coefficient is considered when, in addition to initial and boundary conditions, a solution at the final moment of time is given. Existence and uniqueness results are proven, and a numerical method for the explicit determination of the solution to the said inverse problem is also developed.


35R30 Inverse problems for PDEs
35K55 Nonlinear parabolic equations
65M30 Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs
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