Blow-up and continuation of solutions for some semilinear parabolic equations with nonlinear boundary conditions

Otani Abstract: The following semilinear parabolic equations with nonlinear boundary conditions is studied: ut = u qu 2q 1 in B1 (0;T ), @ u = juj q 1 u on @B1 (0;T ), where B1 R n is the unit ball and q > 1. The nite time blow-up as well as a continuation of blow-up solutions beyond the blow-up time are discussed for the multidimensional case. It is revealed that the behavior of solutions for the multidimensional case diers from that of the one dimensional case.