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Huang, T. and Zhang, S. (2021) Uniform Lipschitz Bound for a Competition Diffusion Advection System with Strong Competition. Applied Mathematics, 12, 383-398.
https://doi.org/10.4236/am.2021.125027

has been cited by the following article:

• TITLE: Uniform Hölder Bounds for Competition Systems with Strong Interaction on a Subdomain

  AUTHORS: Jiahao Ni, Shan Zhang

  KEYWORDS: Singularly Perturbation, Subdomain, Free Boundary Problem, Liouville Type Theorem

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.11 No.6, June 7, 2023

  ABSTRACT: We prove the uniform Hölder bounds of solutions to a singularly perturbed elliptic system arising in competing models in population dynamics. In this system, two species compete to some extent throughout the whole domain but compete strongly on a subdomain. The proof relies upon the blow up technique and the monotonicity formula by Alt, Caffarelli and Friedman.