Classical solvability of multidimensional two-phase Stefan problem for degenerate parabolic equations

TL;DR

This paper proves the local-in-time existence of smooth solutions for a multidimensional two-phase Stefan problem involving degenerate parabolic equations, extending classical results to more complex, porous medium-type equations.

Contribution

It establishes the existence of smooth solutions and natural boundary conditions for the two-phase Stefan problem with degenerate parabolic equations, advancing the mathematical theory in this area.

Findings

Proved local existence of smooth solutions

Established natural Hölder class boundary conditions

Extended classical Stefan problem results to degenerate equations

Abstract

We prove locally in time the existence of a smooth solution for multidimensional two-phase Stefan problem for degenerate parabolic equations of the porous medium type. We establish also natural H\"{o}lder class for the boundary conditions in the Cauchy-Dirichlet problem for a degenerate parabolic equation.