ABSTRACT
For the stability of degenerate parabolic equations, the usual boundary value condition may be overdetermined. How to find an optimal partial boundary value condition has been a long-standing problem. In this paper, we develop the weak characteristic function method to establish a reasonable partial boundary value condition, no matter whether the spatial variable domain Ω is bounded or unbounded. By means of the Kruzkov bi-variables method, the stability of entropy solutions dependent on this partial boundary value condition is proved.
Disclosure statement
No potential conflict of interest was reported by the author(s).