On blow‐up and asymptotic behavior of solutions to a nonlinear parabolic equation of second order

Abstract

We obtain some sufficient conditions under which solutions to a nonlinear parabolic equation of second order with nonlinear boundary conditions exist globally 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.