Finite-time blow-up and global solutions for some nonlinear parabolic equations. (English) Zbl 1150.35336

Gazzola, Filippo

Differ. Integral Equ. 17, No. 9-10, 983-1012 (2004).

Summary: The global existence and finite-time blow-up depending on the initial datum are established for a class of semilinear parabolic equations. The proofs involve tools from the potential-well theory, from the critical-point theory, and from classical comparison principles.

MSC:

35B40	Asymptotic behavior of solutions to PDEs
35K55	Nonlinear parabolic equations

Keywords:

nonlinear parabolic equation; global existence; finite time blow-up