Skip to content
DraconiticResearch
Search Sources API
186,546 studies31 sourcesUpdated 50 min ago
PreprintarXiv licencearXiv

A variational model with finite carrying capacity for segregated multi-species populations in the whole Euclidean space

  • Pu-Zhao Kow
  • Chang-Hong Wu
Open at sourcePDFDOICite

Abstract

We study a variational problem motivated by models of multiple segregated species in a nonhomogeneous environment. The analysis combines tools from potential theory, in particular free boundary methods. The main novelty is that we formulate the variational problem in the whole Euclidean space while imposing a finite carrying capacity constraint, which allows us to investigate saturated regions where the species attain their maximal density. In addition, we provide a modeling interpretation of the constrained energy. We show that it arises as the variational limit of energies with increasingly strong crowding and interspecific competition penalties, in the sense that, regardless of their relative rates, every sequence of minimizers of the penalized energies admits a subsequence that converges strongly to a minimizer of the constrained energy.

Related

  1. Speed and stability of segregated waves in a pressure-based model of heterogeneous cell populations
    Carles Falcó, Rebecca M. Crossley, Martina Conte +1
    arXivPreprintCC BY 4.0Full textCell biologyAnalysis & PDEsarXiv
  2. Lp-Integral Affine Surface Area-Variational Capacity Inequalities
    Yibin Feng, Ding Zhang
    arXivPreprintCC BY 4.0Full textGeometry & topologyarXiv
  3. Variational Bayes for Variable Selection with Adaptive Sharing across Populations and Responses
    Yuehan Yang, Pengfei Chen, Fan Yang +1
    arXivPreprintarXiv licenceFull textStatisticsarXiv
  4. A Comparative Study of Finite-Volume-based Coupled and Segregated Reduced-Order Models for Incompressible Flows in Parametrized Domains
    Andrea Buffolini, Davide Oberto, Gianluigi Rozza
    arXivPreprintCC BY 4.0Full textNumerical analysis & scientific computingFluid dynamicsarXiv
  5. On the existence of smooth varieties of any dimension carrying no Ulrich bundles for some very ample line bundle
    Angelo Felice Lopez
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{kow2026variational,
  title = {{A variational model with finite carrying capacity for segregated multi-species populations in the whole Euclidean space}},
  author = {Pu-Zhao Kow and Chang-Hong Wu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.33996},
  eprint = {2610.33996},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.33996},
}
RIS
TY  - UNPB
TI  - A variational model with finite carrying capacity for segregated multi-species populations in the whole Euclidean space
AU  - Pu-Zhao Kow
AU  - Chang-Hong Wu
PY  - 2026
DA  - 2026/10/25
PB  - arXiv
DO  - 10.48550/arxiv.2610.33996
UR  - https://arxiv.org/abs/2610.33996
AB  - We study a variational problem motivated by models of multiple segregated species in a nonhomogeneous environment. The analysis combines tools from potential theory, in particular free boundary methods. The main novelty is that we formulate the variational problem in the whole Euclidean space while imposing a finite carrying capacity constraint, which allows us to investigate saturated regions where the species attain their maximal density. In addition, we provide a modeling interpretation of the constrained energy. We show that it arises as the variational limit of energies with increasingly strong crowding and interspecific competition penalties, in the sense that, regardless of their relative rates, every sequence of minimizers of the penalized energies admits a subsequence that converges strongly to a minimizer of the constrained energy.
ER  -