✦ LIBER ✦
An inverse source problem with single Dirichlet type measured output data for a linear parabolic equation
✍ Scribed by Alemdar Hasanov
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 226 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0893-9659
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✦ Synopsis
The problem of determining an unknown source term in a linear parabolic equation (x, t) ∈ Ω T , from the Dirichlet type measured output data h(t) := u(0, t) is studied. A formula for the Fréchet gradient of the cost functional J(F ) = ‖u(0, t; F )-h(t)‖ 2 is derived via the solution of the corresponding adjoint problem, within the weak solution theory for PDEs and the quasi-solution approach. The Lipschitz continuity of the gradient is proved. Based on the obtained results the convergence theorem for the gradient method is proposed.