Related papers: Spreading speeds for multidimensional reaction-dif…
This paper is concerned with the propagation phenomenon of the combustion reaction-diffusion equations in domains with multiple cylindrical branches. We first show that there is an entire solution emanating from planar traveling fronts in…
In this paper we study the invasion fronts of spatially periodic monotone reaction-diffusion systems in a multi-dimensional setting. We study the pulsating traveling waves that connect the trivial equilibrium, for which all components of…
This paper is concerned with a time periodic competition-diffusion system \begin{equation*} \begin{cases} {u_t}={u_{xx}}+u(r_1(t)-a_1(t)u-b_1(t)v),\quad t>0,~x\in \mathbb R, {v_t}=d{v_{xx}}+v(r_2(t)-a_2(t)u-b_2(t)v),\quad t>0,~x\in \mathbb…
We describe the resulting spatiotemporal dynamics when a homogeneous equilibrium loses stability in a spatially extended system. More precisely, we consider reaction-diffusion systems, assuming only that the reaction kinetics undergo a…
Spontaneous pattern formation in living systems is driven by reaction-diffusion chemistry and active mechanics. The feedback between chemical and mechanical forces is often essential to robust pattern formation, yet it remains poorly…
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…
Inspired by recent studies associating shifting temperature conditions with changes in the efficiency of predator species in converting their prey to offspring, we propose a predator-prey model of reaction-diffusion type to analyze the…
The current paper is devoted to the study of existence and non-existence of transition fronts for two species competition lattice system in random media, and explore the influence of randomness of the media on the wave profiles and wave…
We prove existence, uniqueness, and stability of transition fronts (generalized traveling waves) for reaction-diffusion equations in cylindrical domains with general inhomogeneous ignition reactions. We also show uniform convergence of…
We consider a family of controlled reaction-diffusion equations, describing the spatial spreading of an invasive biological species. For a given propagation speed $c\in{I\!\!R}$, we seek a control with minimum cost, which achieves a…
Self-activation coupled to a transport mechanism results in traveling waves that describe polymerization reactions, forest fires, tumor growth, and even the spread of epidemics. Diffusion is a simple and commonly used model of particle…
In this paper, we study the propagation dynamics for a class of integrodifference competition models in a periodic habitat. An interesting feature of such a system is that multiple spreading speeds can be observed, which biologically means…
The fast-reaction limit for reaction--diffusion systems modelling predator--prey interactions is investigated. In the considered model, predators exist in two possible states, namely searching and handling. The switching rate between these…
In this paper we investigate some free boundary problems for the Lotka-Volterra type prey-predator model in one space dimension. The main objective is to understand the asymptotic behavior of the two species (prey and predator) spreading…
This article investigates a mathematical model for bushfire propagation, focusing on the existence and properties of translating solutions. We obtain quantitative bounds on the environmental diffusion coefficient and ignition kernels,…
We study reaction-diffusion systems where diffusion is by jumps whose sizes are distributed exponentially. We first study the Fisher-like problem of propagation of a front into an unstable state, as typified by the A+B $\to$ 2A reaction. We…
This paper is concerned with the interaction between a planar traveling front and a compact obstacle for monotone bistable reaction-diffusion systems in exterior domains. By constructing appropriate sub- and supersolutions, we first…
Reaction-diffusion systems with cross-diffusion terms in addition to, or instead of, the usual self-diffusion demonstrate interesting features which motivate their further study. The present work is aimed at designing a toy…
We consider a spatially distributed population dynamics model with excitable predator-prey dynamics, where species propagate in space due to their taxis with respect to each other's gradient in addition to, or instead of, their diffusive…
We study a reaction-diffusion system of partial differential equations, which can be taken to be a basic model for criminal activity. We show that the assumption of a populations natural tendency towards crime significantly changes the…