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Identification of the diffusion in a nonlinear parabolic problem and numerical resolution
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 twodimensional 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 casedoi:10.21914/anziamj.v57i0.8835 fatcat:jl74qjwdkncczihhduu5ni5qe4