Elliptic regularization for the heat equation with nonlinear boundary conditions

Abstract

The paper is devoted to an elliptic perturbation of a parabolic problem. The solution v of the heat equation with a nonlinear boundary condition is compared with the solution v_ε of an elliptic regularization. An asymptotic expansion of v_ε is constructed and the order of accuracy for the difference v_ε−v is obtained. The boundary function method by Vishik and Lyusternik is used.