New approach to identify the initial condition in degenerate hyperbolic equation |
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Authors: | K Atifi EL-H Essoufi B Khouiti |
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Affiliation: | Laboratoire de Mathmatiques, Informatique et Sciences de l’ingénieur (MISI), Université Hassan 1 , Settat, Morocco |
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Abstract: | This paper deals with the determination of an initial condition in degenerate hyperbolic equation from final observations. With the aim of reducing the execution time, this inverse problem is solved using an approach based on double regularization: a Tikhonov’s regularization and regularization in equation by viscose-elasticity. So, we obtain a sequence of weak solutions of degenerate linear viscose-elastic problems. Firstly, we prove the existence and uniqueness of each term of this sequence. Secondly, we prove the convergence of this sequence to the weak solution of the initial problem. Also we present some numerical experiments to show the performance of this approach. |
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Keywords: | Data assimilation adjoint method regularization wave equation inverse problem degenerate equations optimization |
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