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Volume 16,     Number 1,     Spring 2008

 

DYNAMICS OF A QUASILINEAR REACTION
DIFFUSION EQUATION WITH SINGULAR
REACTION FUNCTIONS
C. V. PAO AND W. H. RUAN

Abstract. Degenerate reaction-diffusion equations of porous-medium type with singular reaction functions in both the differential equation and the boundary condition are investigated. The aim of this paper is to show the existence of a unique global time-dependent solution, the existence and uniqueness of a positive steady-state solution, and the convergence of the time-dependent solution to the positive steady-state solution. The convergence result of the time dependent solution exhibits some rather interesting distinctive behavior when compared with density-independent diffusion.

 

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