Please use this identifier to cite or link to this item: https://hdl.handle.net/1959.11/31817
Title: The Stefan problem for the Fisher-KPP equation with unbounded initial range
Contributor(s): Ding, Weiwei (author); Du, Yihong  (author)orcid ; Guo, Zongming (author)
Publication Date: 2021-04
Early Online Version: 2021-04-05
DOI: 10.1007/s00526-020-01877-4
Handle Link: https://hdl.handle.net/1959.11/31817
Abstract: 

We consider the nonlinear Stefan problem

{ut-dΔu = au − bu2 for  x Ω(t), t > 0,
u = 0 and ut = μ|∇xu|2for  x ∂Ω(t), t > 0,
u(0,x) = u0(x) for  x Ω0,

where Ω(0)=Ω0 is an unbounded Lipschitz domain in ℝN, u0 > 0 in Ω0 and u0 vanishes on ∂Ω0. When Ω0 is bounded, the long-time behavior of this problem has been rather well-understood by Du et al. (J Differ Equ 250:4336-4366, 2011; J Differ Equ 253:996-1035, 2012; J Ellip Par Eqn 2:297-321, 2016; Arch Ration Mech Anal 212:957-1010, 2014). Here we reveal some interesting different behavior for certain unbounded Ω0. We also give a unified approach for a weak solution theory to this kind of free boundary problems with bounded or unbounded Ω0.

Publication Type: Journal Article
Source of Publication: Calculus of Variations and Partial Differential Equations, 60(2), p. 1-37
Publisher: Springer
Place of Publication: Germany
ISSN: 1432-0835
0944-2669
Fields of Research (FoR) 2020: 490410 Partial differential equations
Socio-Economic Objective (SEO) 2020: 280118 Expanding knowledge in the mathematical sciences
Peer Reviewed: Yes
HERDC Category Description: C1 Refereed Article in a Scholarly Journal
Appears in Collections:Journal Article
School of Science and Technology

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