Asymptotic behavior of solutions of a semilinear heat equation with localized reaction. (English) Zbl 1198.35128

Suzuki, Ryuichi

Adv. Differ. Equ. 15, No. 3-4, 283-314 (2010).

The author considers non-negative solutions to the Dirichlet problem to a semilinear heat equation with localized reaction, and he shows that an unbounded global solution (infinite time blow-up solution) exists.

Reviewer: Jiaqi Mo (Wuhu)

MSC:

35K58	Semilinear parabolic equations
35B40	Asymptotic behavior of solutions to PDEs
35B35	Stability in context of PDEs
35B45	A priori estimates in context of PDEs
35K20	Initial-boundary value problems for second-order parabolic equations
35K57	Reaction-diffusion equations

Keywords:

non-negative solutions; Dirichlet problem; infinite time blow-up solution