A FREE BOUNDARY PROBLEM FOR A QUASILINEAR REACTION-DIFFUSION EQUATION APPEARING IN ECOLOGY.

In this paper, we study a quasilinear parabolic equation with free boundary. A priori estimates of the H¨older norms are established. On the basic of a priori estimates, the existence and uniqueness of the solution is proved. Furthermore, we consider spreading-vanishing dichotomy result with advection term, specifically the species either successfully spreads to the infinity as t → ∞, or it fails to establish and does out in the long run. [ABSTRACT FROM AUTHOR]