Solving coefficient inverse problems for nonlinear singularly perturbed equations of the reaction-diffusion-advection type with data on the position of a reaction front
2021
Abstract An approach to solving coefficient inverse problems for nonlinear reaction-diffusion-advection equations is proposed. As an example, we consider an inverse problem of restoring a coefficient in a nonlinear Burgers-type equation. One of the features of the inverse problem is a use of additional information about the position of a reaction front. Another feature of the approach is a use of asymptotic analysis methods to select a good initial guess in a gradient method for minimizing a cost functional that occurs when solving the coefficient inverse problem. Numerical experiments demonstrate the effectiveness of the proposed approach.
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