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) ; 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: |
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{ | ut-dΔu = au − bu2 | for x Ω(t), t > 0, |
u = 0 and ut = μ|∇xu|2 | for 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.
0944-2669
School of Science and Technology
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