Features of numerical reconstruction of a boundary condition in an inverse problem for a reaction–diffusion–advection equation with data on the position of a reaction front
Abstract:
A new approach to the reconstruction of a boundary condition in an inverse problem for a nonlinear singularly perturbed reaction–diffusion–advection equation with data on the reaction front position is proposed. The problem is solved via gradient minimization of a cost functional with an initial approximation chosen by applying asymptotic analysis methods. The efficiency of the proposed approach is demonstrated by numerical experiments.
Key words:inverse problem with data on the position of a reaction front, inverse boundary value problem, reaction–diffusion–advection equation.