BLOW-UP BEHAVIOR FOR A QUASILINEAR PARABOLIC EQUATION WITH NONLINEAR BOUNDARY CONDITION

(Communicated by Aim Sciences) Abstract. In this paper, we study the solution of an initial boundary value problem for a quasilinear parabolic equation with a nonlinear boundary con-dition. We first show that any positive solution blows up in finite time. For a monotone solution, we have either the single blow-up point on the boundary, or blow-up on the whole domain, depending on the parameter range. Then, in the single blow-up point case, the existence of a unique self-similar profile is proven. Moreover, by constructing a Lyapunov function, we prove the conver-gence of the solution to the unique self-similar solution as t approaching the blow-up time