Abstract:We obtain some sufficient conditions under which solutions to a nonlinear parabolic equation of second order with nonlinear boundary conditions tend to zero or blow up in a finite time. We also give the asymptotic behavior of solutions which tend to zero as $t\rightarrow \infty $. Finally, we obtain the asymptotic behavior near the blow-up time of certain blow-up solutions and describe their blow-up set.
Keywords: blow-up, global existence, asymptotic behavior, maximum principle
AMS Subject Classification: 35K55, 35K60, 35B40