Convergence in the H\"older space of the solutions of the problems for the parabolic equations with two small parameters in a~boundary

G. I. Bizhanova

Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 46, Tome 459 (2017), pp. 7-36

Résumé

Multidimensional two-phase problem for the parabolic equations with two small parameters $\varepsilon>0$ and $\kappa>0$ at the principal terms in the conjugation condition is studied in the Hölder space. An estimate of the perturbed term – time derivative is derived. Its proved that the solution of the problem converges as $\varepsilon>0$ the solution of the problem as $\kappa\to0$, $\varepsilon>0$; $\varepsilon\to0$, $\kappa>0$; $\varepsilon=0$, $\kappa\to0$ without loss of the smoothness of the given functions.