Abstract:

The problem of recovery the initial condition in the initial boundary value problem for the nonlinear diffusion-reaction type equation on the basis of noisy data of integral type at fixed times is incorrect (inverse problem). In this paper the solution of the inverse problem is reduced to the solution of the problem of minimisation of the A.N. Tikhonov functional, in which the regularisation parameter is determined in various ways. Numerical analysis of regularised solutions of the inverse problem for linear and nonlinear formulation is given, the efficiency of regularisation of the numerical solution at a fixed noise level in the data is shown.