A FREE BOUNDARY PROBLEM ON 2-D SPATIAL DOMAIN EXHIBITING FINGERING\ast

Chuncheng Wang; Chunxi Feng; Mark Lewis; Hao Wang

doi:10.1137/25M1762592

A FREE BOUNDARY PROBLEM ON 2-D SPATIAL DOMAIN EXHIBITING FINGERING^\ast

Chuncheng Wang
, Chunxi Feng
, Mark Lewis
, Hao Wang^*

^*Corresponding author for this work

School of Mathematics

Harbin Institute of Technology
University of Victoria BC

Research output: Contribution to journal › Article › peer-review

Abstract

We study the population dynamics of a single species modeled by a Fisher-KPP equation with an integral weighted free boundary condition in a two dimensional region. The spatial domain of the model is a rectangle with one side having a moving boundary and the remaining three sides fixed. We prove the global existence and uniqueness of solution, and show the vanishing-balancing-spreading trichotomy dynamics of the model. By numerical simulation, the steady states exhibit a finger-shaped front pattern, a long-lasting topic of interest in spatial ecology. For certain sets of parameters, the finger-shaped free boundary could vary over time.

Original language	English
Pages (from-to)	1403-1421
Number of pages	19
Journal	SIAM Journal on Applied Mathematics
Volume	86
Issue number	4
DOIs	https://doi.org/10.1137/25M1762592
State	Published - 2026

Keywords

free boundary problem
front pattern
vanishing-balancing-spreading trichotomy

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10.1137/25M1762592

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title = "A FREE BOUNDARY PROBLEM ON 2-D SPATIAL DOMAIN EXHIBITING FINGERING\textbackslash{}ast",

abstract = "We study the population dynamics of a single species modeled by a Fisher-KPP equation with an integral weighted free boundary condition in a two dimensional region. The spatial domain of the model is a rectangle with one side having a moving boundary and the remaining three sides fixed. We prove the global existence and uniqueness of solution, and show the vanishing-balancing-spreading trichotomy dynamics of the model. By numerical simulation, the steady states exhibit a finger-shaped front pattern, a long-lasting topic of interest in spatial ecology. For certain sets of parameters, the finger-shaped free boundary could vary over time.",

keywords = "free boundary problem, front pattern, vanishing-balancing-spreading trichotomy",

author = "Chuncheng Wang and Chunxi Feng and Mark Lewis and Hao Wang",

note = "Publisher Copyright: Copyright {\textcopyright} by SIAM. Unauthorized reproduction of this article is prohibited.",

year = "2026",

doi = "10.1137/25M1762592",

language = "英语",

volume = "86",

pages = "1403--1421",

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AU - Feng, Chunxi

AU - Lewis, Mark

AU - Wang, Hao

PY - 2026

Y1 - 2026

N2 - We study the population dynamics of a single species modeled by a Fisher-KPP equation with an integral weighted free boundary condition in a two dimensional region. The spatial domain of the model is a rectangle with one side having a moving boundary and the remaining three sides fixed. We prove the global existence and uniqueness of solution, and show the vanishing-balancing-spreading trichotomy dynamics of the model. By numerical simulation, the steady states exhibit a finger-shaped front pattern, a long-lasting topic of interest in spatial ecology. For certain sets of parameters, the finger-shaped free boundary could vary over time.

AB - We study the population dynamics of a single species modeled by a Fisher-KPP equation with an integral weighted free boundary condition in a two dimensional region. The spatial domain of the model is a rectangle with one side having a moving boundary and the remaining three sides fixed. We prove the global existence and uniqueness of solution, and show the vanishing-balancing-spreading trichotomy dynamics of the model. By numerical simulation, the steady states exhibit a finger-shaped front pattern, a long-lasting topic of interest in spatial ecology. For certain sets of parameters, the finger-shaped free boundary could vary over time.

KW - free boundary problem

KW - front pattern

KW - vanishing-balancing-spreading trichotomy

UR - https://www.scopus.com/pages/publications/105045226075

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M3 - 文章

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JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

IS - 4

ER -

A FREE BOUNDARY PROBLEM ON 2-D SPATIAL DOMAIN EXHIBITING FINGERING^\ast

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Keywords

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