Takhirov, Zh. O.; Turaev, R. N. The nonlocal Stefan problem for quasilinear parabolic equation. (Russian. English summary) Zbl 1326.35423 Vestn. Samar. Gos. Tekh. Univ., Ser. Fiz.-Mat. Nauki 2012, No. 3(28), 8-16 (2012). 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. Cited in 4 Documents 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 Keywords:nonlocal problem; Stefan problem; quasilinear parabolic equation; free boundary; a priori estimates; existence and uniqueness theorem; fixed boundary; method of potentials; maximum principle × Cite Format Result Cite Review PDF Full Text: DOI MNR