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

Article type: Research Article

Authors: Boni, Théodore K.

Affiliations: Université Paul Sabatier, UFR‐MIG, MIP, 118 route de Narbonne, 31062 Toulouse, France E‐mail: boni@mip.ups‐tlse.fr

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.

Keywords: Blow‐up, global existence, asymptotic behavior, maximum principle

Journal: Asymptotic Analysis, vol. 21, no. 3‐4, pp. 187-208, 1999