The Stefan problem for the Fisher-KPP equation with unbounded initial range

Title
The Stefan problem for the Fisher-KPP equation with unbounded initial range
Publication Date
2021-04
Author(s)
Ding, Weiwei
Du, Yihong
( author )
OrcID: https://orcid.org/0000-0002-1235-0636
Email: ydu@une.edu.au
UNE Id une-id:ydu
Guo, Zongming
Type of document
Journal Article
Language
en
Entity Type
Publication
Publisher
Springer
Place of publication
Germany
DOI
10.1007/s00526-020-01877-4
UNE publication id
une: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.

Link
Citation
Calculus of Variations and Partial Differential Equations, 60(2), p. 1-37
ISSN
1432-0835
0944-2669
Start page
1
End page
37

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