Identification of the diffusion in a nonlinear parabolic problem and numerical resolution

Sameh Abidi, Jamil Satouri


This paper presents an iterative method to identify the diffusion in a semi-linear parabolic problem. This method can be generalized to other kind of problems, elliptic, parabolic and hyperbolic in two-dimensional and three-dimensional case. The diffusion is obtained by solving an optimal control problem. By imposing specific conditions to the data, we build a sequence of linear problems which converge to the exact solution. We discretize our problem by a finite element method in the first case and a spectral method in the second case, using the sensibility method for approximating the gradient of the functional. Some numerical experiments prove the efficiency of this method.

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Parabolic equation, Diffusion, Optimization, Finite-elements, Spectral method.

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