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Null controllability of degenerate/singular parabolic equations with degeneracy and singularity occurring in the interior of the spatial domain
Kh. Atifi, E.-H. Essoufi, B. Khouiti Faculté des Sciences et Techniques, Université Hassan 1er, Laboratoire MISI, B.P. 577, Settat 26000, Morocco
Abstract:
The main purpose of this work is to study numerically a null controllability for a class of one-dimensional degenerate/singular parabolic equations, in divergence and nondivergence form. For this, we resolve an inverse source problem reformulated in a least-squares framework, which leads to a non-convex minimization problem of a cost function J, that is solved using a Tikhonov regularization. Firstly, we prove the well-posedness of the minimization problem and the direct problem. Secondly we prove the differentiability of the functional J, which gives the existence of the gradient of J, that is computed using the adjoint state method. Finally, to show the convergence of the descent method, we prove the Lipschitz continuity of the gradient of J. Also we present some numerical experiments.
Keywords:
Null controllability, singular equations, inverse source problem, adjoint-state method.
Citation:
Kh. Atifi, E.-H. Essoufi, B. Khouiti, “Null controllability of degenerate/singular parabolic equations with degeneracy and singularity occurring in the interior of the spatial domain”, Eurasian Journal of Mathematical and Computer Applications, 8:1 (2020), 4–29
Linking options:
https://www.mathnet.ru/eng/ejmca148 https://www.mathnet.ru/eng/ejmca/v8/i1/p4
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Abstract page: | 253 | Full-text PDF : | 73 | References: | 1 |
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