Propagation and reaction–diffusion models with free boundaries

Y Du - Bulletin of Mathematical Sciences, 2022 - World Scientific
In this short survey, we describe some recent developments on the modeling of propagation
by reaction-differential equations with free boundaries, which involve local as well as …

Two species nonlocal diffusion systems with free boundaries

Y Du, M Wang, M Zhao - arXiv preprint arXiv:1907.04542, 2019 - arxiv.org
We study a class of free boundary systems with nonlocal diffusion, which are natural
extensions of the corresponding free boundary problems of reaction diffusion systems. As …

Invasion of open space by two competitors: spreading properties of monostable two‐species competition‐diffusion systems

L Girardin, KY Lam - Proceedings of the London Mathematical …, 2019 - Wiley Online Library
This paper is concerned with some spreading properties of monostable Lotka–Volterra two‐
species competition‐diffusion systems when the initial values are null or exponentially …

Spreading speed for a West Nile virus model with free boundary

Z Wang, H Nie, Y Du - Journal of Mathematical Biology, 2019 - Springer
The purpose of this paper is to determine the precise asymptotic spreading speed of the
virus for a West Nile virus model with free boundary, introduced recently in Lin and Zhu (J …

Spreading speed of a degenerate and cooperative epidemic model with free boundaries.

M Zhao, WT Li, W Ni - Discrete & Continuous Dynamical …, 2020 - search.ebscohost.com
This paper deals with the spreading speed of the disease described by a partially
degenerate and cooperative epidemic model with free boundaries. We show that the …

Long-time dynamics of a diffusive epidemic model with free boundaries.

R Wang, Y Du - … & Continuous Dynamical Systems-Series B, 2021 - search.ebscohost.com
In this paper, we determine the long-time dynamical behaviour of a reaction-diffusion system
with free boundaries, which models the spreading of an epidemic whose moving front is …

The dynamics of a Lotka-Volterra competition model with nonlocal diffusion and free boundaries

JF Cao, WT Li, J Wang, M Zhao - 2021 - projecteuclid.org
This paper is concerned with a Lotka-Volterra competition model with nonlocal diffusion and
free boundaries, which describes the evolution of an invasive species with free boundaries …

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach

Q Liu, S Liu, KY Lam - arXiv preprint arXiv:1908.05025, 2019 - arxiv.org
We establish spreading properties of the Lotka-Volterra competition-diffusion system. When
the initial data vanish on a right half-line, we derive the exact spreading speeds and prove …

Stacked invasion waves in a competition-diffusion model with three species

Q Liu, S Liu, KY Lam - Journal of Differential Equations, 2021 - Elsevier
We investigate the spreading properties of a three-species competition-diffusion system,
which is not order-preserving. We apply the Hamilton-Jacobi approach, due to Freidlin …

[HTML][HTML] Asymptotic spreading of a diffusive competition model with different free boundaries

S Liu, H Huang, M Wang - Journal of Differential Equations, 2019 - Elsevier
Abstract Recently, the authors of [22] studied a diffusive prey–predator model with two
different free boundaries. They first obtained the existence, uniqueness, regularity, uniform …