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

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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… Click to show full 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: partial boundary; reaction diffusion; unbounded domain

Journal Title: Journal of Inequalities and Applications
Year Published: 2019

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