ASYMPTOTIC BEHAVIOUR OF SOLUTIONS OF A QUASILINEAR PARABOLIC EQUATION WITH ROBIN BOUNDARY CONDITION

In this paper we study solutions of the quasi-linear parabolic equations partial derivative u/partial derivative t - Delta(p)u = a(x)vertical bar u vertical bar(q-1)u in (0, T) x Omega with Robin boundary condition partial derivative u/partial derivative v vertical bar del u vertical bar(p-2) = b(x)vertical bar u vertical bar(r-1)u in (0, T) x partial derivative Omega where Omega is a regular bounded domain in R-N N >= 3, q > 1, r > 1 and p >= 2. Some sufficient conditions on a and b are obtained for those solutions to be bounded or blowing up at a finite time. Next we give the asymptotic behavior of the solution in special cases.