相关论文: Rigorous fast signal diffusion limit and convergen…
To understand the spreading and interaction of prey and predator, in this paper we study the dynamics of the diffusive Lotka-Volterra type prey-predator model with different free boundaries. These two free boundaries, which may intersect…
This study examines a fully parabolic predator-prey chemo-alarm-taxis system under homogeneous Neumann boundary conditions in a bounded domain $\Omega \subset \mathbb{R}^n$ with a smooth boundary $\partial\Omega$. Under specific parameter…
This paper investigates the spreading properties of globally defined bounded positive solutions of a chemotaxis system featuring a logistic source and consumption: \[ \left\{ \begin{aligned} &\partial_tu=\Delta u - \chi\nabla\cdot(u\nabla…
In this paper we investigate the dynamical properties of a spatially periodic reaction-diffusion system {whose reaction terms are of hybrid nature in the sense that they are partly competitive and partly cooperative depending on the value…
We investigate the Lotka-Volterra model for predator-prey competition with a finite carrying capacity that varies periodically in time, modeling seasonal variations in nutrients or food resources. In the absence of time variability, the…
This paper investigates the dynamics of a reaction-diffusion system with two free boundaries, modeling the invasion of two cooperative species, where the free boundaries represent expanding fronts. We first analyze the long-term behavior of…
We propose and analyse numerical schemes for a system of quasilinear, degenerate evolution equations modelling biofilm growth as well as other processes such as flow through porous media and the spreading of wildfires. The first equation in…
We investigate a fast-reaction--diffusion system modelling the effect of autotoxicity on plant-growth dynamics, in which the fast-reaction terms are based on the dichotomy between healthy and exposed roots depending on the toxicity. The…
This paper is concerned with a diffusive Lotka-Volterra type competition system with a free boundary in one space dimension. Such a system may be used to describe the invasion of a new species into the habitat of a native competitor. We…
Chemical kinetics plays an important role in governing the thermal evolution in reactive flows problems. The possible interactions between chemical species increase drastically with the number of species considered in the system. Various…
This paper investigates a class of chemotaxis systems modeling lethal interactions in a smooth, bounded domain $\Omega \subset \mathbb{R}^n$ with homogeneous Neumann boundary conditions. We examine two distinct cases: (i) a fully parabolic…
In this paper, we consider two species chemotaxis systems with Lotka-Volterra competition reaction terms. Under appropriate conditions on the parameters in such a system, we establish the existence of traveling wave solutions of the system…
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 before the free boundary represents the spreading front of the…
Previously derived "global" thermodynamic speed limit theorems state that increasing the maximum speed with which a system can evolve between two given probability distributions over its states requires the system to produce more entropy in…
We study the effects of fast spatial movement of molecules on the dynamics of chemical species in a spatially heterogeneous chemical reaction network using a compartment model. The reaction networks we consider are either single- or…
In this paper we consider the diffusive competition model with free boundary in the heterogeneous time-periodic environment, in which the variable intrinsic growth rates of invasive and native species may change signs and be "very negative"…
In this paper we study the existence of solutions of a parabolic-elliptic system of partial differential equations describing the behaviour of a biological species $u$ and a chemical stimulus $v$ in a bounded and regular domain $\Omega$ of…
We consider adaptive change of diet of a predator population that switches its feeding between two prey populations. We develop a novel 1 fast--3 slow dynamical system to describe the dynamics of the three populations amidst continuous but…
Classical theory predicts that for two competing populations subject to a constant downstream drift, the faster disperser will competitively exclude the slower disperser. In the current work, we consider a novel model of a "much faster"…
This paper proposes a novel reaction-diffusion system approximation tailored for singular diffusion problems, typified by the fast diffusion equation. While such approximation methods have been successfully applied to degenerate parabolic…