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The nonlocal Stefan problem for quasilinear parabolic equation. (Russian. English summary) Zbl 1326.35423

Summary: In this paper, we deal with a free boundary problem with nonlocal boundary condition for a quasilinear parabolic equation. For the solutions of the problem a priori estimates of Schauder’s type are established. On the base of a priori estimates the existence and uniqueness theorems are proved.

MSC:

35R35 Free boundary problems for PDEs
35K05 Heat equation
35R05 PDEs with low regular coefficients and/or low regular data
35B45 A priori estimates in context of PDEs
35B50 Maximum principles in context of PDEs