J. O. Takhirov, R. N. Turaev, “The nonlocal Stefan problem for quasilinear parabolic equation”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2012, Issue 3(28),Pages <nobr>8

This article is cited in 3 papers

Differential Equations

The nonlocal Stefan problem for quasilinear parabolic equation

J. O. Takhirov^a, R. N. Turaev^b

^a Nizami Tashkent State Pedagogical University, Tashkent, Uzbekistan
^b Institute for Mathematics and Information Technologies of the National Academy of Sciences of Uzbekistan, Tashkent, Uzbekistan

Abstract: In this paper, we deal with free boundary problem with nonlocal boundary condition for quasilinear parabolic equation. For the solutions of the problem apriory estimates of Shauder's type are established. On the base of apriory estimations the existence and uniqueness theorems are proved

Keywords: nonlocal problem, Stefan problem, quasilinear parabolic equation, free boundary, priori estimates, existence and uniqueness theorem, fixed boundary, method of potentials, maximum principle.

UDC: 517.956.45

MSC: Primary 35R35; Secondary 35K05, 35R05

Original article submitted 10/VIII/2011
revision submitted – 19/XII/2011

DOI: 10.14498/vsgtu1010