Determination of a time-dependent heat source under nonlocal boundary and integral overdetermination conditions
Copyright policy )Determination of a time-dependent heat source under nonlocal boundary and integral overdetermination conditions
The authors investigate the inverse problem of finding a time-dependent heat source in a parabolic equation with nonlocal boundary and integral over-determination conditions. Under some natural regularity and consistency conditions on the input data the well-posedness of the problem is shown by using the generalized Fourier method. Numerical tests using the Crank-Nicolson finite difference scheme combined with an iterative method are presented and discussed.
- University of Kocaeli Turkey
- Gebze Technical University Turkey
- University of Leeds United Kingdom
Inverse problems for PDEs, numerical examples, heat source, parabolic equation, mollification method, Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs, Initial-boundary value problems for second-order parabolic equations, Finite difference methods for initial value and initial-boundary value problems involving PDEs, integral overdetermination condition, inverse problem, Crank-Nicolson, Fourier method, finite difference method
Inverse problems for PDEs, numerical examples, heat source, parabolic equation, mollification method, Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs, Initial-boundary value problems for second-order parabolic equations, Finite difference methods for initial value and initial-boundary value problems involving PDEs, integral overdetermination condition, inverse problem, Crank-Nicolson, Fourier method, finite difference method
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