The entropy solution of a reaction–diffusion equation on an unbounded domain

Abstract

Abstract The degenerate parabolic equations from the reaction–diffusion problems are considered on an unbounded domain Ω⊂RN $\varOmega\subset\mathbb {R}^{N}$. It is expected that only a partial boundary should be imposed the homogeneous boundary value, but how to give the analytic expression of this partial boundary seems very difficult. A new method, which is called the general characteristic function method, is introduced in this paper. By this new method, a reasonable analytic expression of the partial boundary value condition is found. Moreover, the stability of the entropy solutions is established based on this partial boundary value condition.

Keywords

• Reaction–diffusion problem
• Unbounded domain
• Partial boundary value condition
• The entropy solution