## Th\'eodore K. Boni

*On blow-up and asymptotic behavior of solutions to a nonlinear parabolic equation of second order with nonlinear boundary conditions *

Comment.Math.Univ.Carolinae 40,3 (1999) 457-475. **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

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