Florin Problem For Quasilinear Diffusion Equation Taking Into Account Nonlinear Convection

Authors

  • R.N.Turaev, K.N.Turaev, U.R.Nortojiev

Abstract

In this paper, we study a problem with a free boundary of the Florin type for a quasilinear parabolic equation taking into account nonlinear convection. First, the original problem is reduced to a problem with a free boundary of Stefan type. A priori estimates of the Schauder type are established. Further, the equivalence of the initial and received tasks is established. On the basis of the established estimates, the behavior of the free boundary investigated in the considered period of time. The uniqueness of the solution to the original problem is proved, and a priori estimates for the highest derivatives are established. As a result, the existence of a solution to the obtained and the original problem is proved using the Schauder fixed point method.

Published

2020-11-01

Issue

Section

Articles