Journal of Inequalities and Applications

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