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

• Main Authors: Huashui Zhan, Yongping Li
• Format: Article
• Language: English
• Published: SpringerOpen 2019-01-01
• Series: Journal of Inequalities and Applications
• Subjects: Reaction–diffusion problem; Unbounded domain; Partial boundary value condition; The entropy solution
• Online Access: http://link.springer.com/article/10.1186/s13660-019-1956-3

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.