Convergence in the Hölder Space of the Solutions to Problems for Parabolic Equations with Two Small Parameters in Boundary Condition

Abstract

Multidimensional two-phase problem for the parabolic equations with two small parameters ε > 0 and κ > 0 at the leading terms in the conjugation condition is studied in the Hölder space. An estimate of the perturbed term, time derivative, is derived. It is proved that the solution to the problem converges as κ → 0 and ε > 0, ε → 0 and κ > 0, and ε = 0 and κ → 0 without loss of the smoothness of given functions.