Volume 16, Number 1, Spring 2008
DYNAMICS OF A QUASILINEAR REACTION
DIFFUSION EQUATION WITH SINGULAR
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.