Solving coefficient inverse problems for nonlinear singularly perturbed equations of the reaction-diffusion-advection type with data on the position of a reaction front

•The data on the position of a reaction front is used for solving the coefficient inverse problem.•The asymptotic analysis methods allow to select a good initial guess in a gradient method for minimizing a cost functional.•This good initial guess for the gradient method under certain conditions can be taken as an approximate solution to the inverse problem itself. 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.