Inverse boundary value problem for nonlinear diffusion equation with non-local time-integral conditions of the second kind2

Abstract

This work deals with the solvability of inverse boundary value problem with time-dependent unknown coefficient for nonlinear diffusion equation. Definition of classical solution for the considered inverse boundary value problem is introduced. By the Fourier method, the problem is reduced to the system of integral equations. Using the contraction mappings method, the existence and uniqueness of the solution of the system of integral equations are proved. Finally, the existence and uniqueness of the classical solution of original problem are proved.