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

The degenerate parabolic equations from the reaction-diffusion problems are considered on an unbounded domain RN. 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.