Quelques Problèmes Aux-limites Gouvernés Par L'opérateur Perturbé Des Ondes Et De La Diffusion

Résumé: This work includes some problems in extreme cases for the partial derivative equations semi linear second-order of hyperbolic type and the dynamic problem of the diffusion. The first category of problems in extreme cases models the propagation of a wave in a homogeneous elastic medium. While the second models the problem of the diffusion which is of parabolic type, where it intervenes in several applications. In the first chapter, one recalled the function analytic, the second and the third chapters, one considered initially, the mathematical model general of the disturbed waves, and one studies particular cases of the problem general. In each case one will be interested in the existence, the unicity and the regularity of the solutions. The techniques used, are those of the method of compactness. The final chapter constitutes an original work; one studied for the first time the problem of the diffusion by the techniques of elliptic regularization. One showed a theorem of existence of a solution of this problem

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