Degenerate parabolic equations with partial boundary value conditions

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.

KEYWORDS:

• Degenerate parabolic equation
• partial boundary value condition
• weak characteristic function method
• entropy solution
• stability

2010 MSCS:

• 35K65
• 35B35
• 35K20

Disclosure statement

No potential conflict of interest was reported by the author(s).