The asymptotic self-similar behavior for the quasilinear heat equation with nonlinear boundary condition

In this paper the quasilinear heat equation with the nonlinear boundary condition is studied. The blow-up rate and existence of a self-similar solution are obtained. It is proved that the rescaled function v.y; t/ D .T 􀀀 t/1=.2pC 􀀀2/u..T 􀀀 t/.p􀀀1/=.2pC 􀀀2/y; t/; behaves as t ! T like a nontrivial self-similar profile.