W.Y. Chan. Quenching for Multi-Dimensional Semilinear Parabolic Problems on a Ball with a Localized Source. Dynamic Systems and Applications 29 (2020) No. 1, 1-10
https://doi.org/10.46719/dsa20202911
ABSTRACT.
We study the quenching set of a multi-dimensional semilinear parabolic problem on a ball subject to the first initial-boundary condition. The source term of this problem is a nonlinear localized function. This function tends to infinity when the solution u approaches a finite number. This mathematical model illustrates a nonlinear reaction of a dynamical system occurring at a single location. The main result of this paper is that u quenches at a single point only and the blow-up set of ut is the whole domain.
Keywords. Localized Source; Quenching; Green’s Function
AMS (MOS) Subject Classification. 35K20, 35K57, 35K58