Partial boundary value condition for a nonlinear degenerate parabolic equation

In this paper, a nonlinear degenerate parabolic equation is considered. By proposing a new partial boundary value condition and constructing special test functions, we prove the stability of the solutions by means of the Kruzkov bi-variables method. Moreover, we show that if there is an interaction between the diffusion term and the convection term, the stability can be established without any boundary value condition. (C) 2019 Elsevier Inc. All rights reserved.