Related papers: Spreading speeds and traveling waves for monotone …
We consider a reaction-diffusion equation in narrow random channels. We approximate the generalized solution to this equation by the corresponding one on a random graph. By making use of large deviation analysis we study the asymptotic wave…
Many reaction-diffusion models produce travelling wave solutions that can be interpreted as waves of invasion in biological scenarios such as wound healing or tumour growth. These partial differential equation models have since been adapted…
For scalar reaction-diffusion equations, a traveling wave is a front which transforms a higher energy state to a lower energy state. The same is true for a system of equations with a gradient structure. At the core of this phenomenon, the…
In this paper, we investigate so-called forced wave solutions of a three components reaction-diffusion system from population dynamics. Our system involves three species that are respectively two competing preys and one predator; moreover,…
We study reaction-diffusion particle systems with several interaction mechanisms. As the number of particles tends to infinity, the system admits a mean-field limit describing the bulk behaviour. We focus on determining the propagation…
Climate change is reshaping species interactions and movement across fragmented landscapes. Despite this, most mathematical models assume random diffusion, overlooking the influence of directed movement. Here, we develop a graph based…
This work presents a generalized physical interpretation of unconventional dispersion asymmetries associated moving elastic solids. By shifting the notion from systems with time-variant material fields to physically traveling materials, the…
Reaction-diffusion processes can be adopted to model a large number of dynamics on complex networks, such as transport processes or epidemic outbreaks. In most cases, however, they have been studied from a fermionic perspective, in which…
We investigate wave propagation in rotationally symmetric tubes with a periodic spatial modulation of cross section. Using an asymptotic perturbation analysis, the governing quasi two-dimensional reaction-diffusion equation can be reduced…
We show that propagation speeds in invasion processes modeled by reaction-diffusion systems are determined by marginal spectral stability conditions, as predicted by the marginal stability conjecture. This conjecture was recently settled in…
Starting from the kinetic approach for a mixture of reacting gases whose particles interact through elastic scattering and a bimolecular reversible chemical reaction, the equations that govern the dynamics of the system are obtained by…
In this paper, we study the existence of traveling wave solutions and the spreading speed for the solutions of an age-structured epidemic model with nonlocal diffusion. Our proofs make use of the comparison principles both to construct…
A key problem in modelling the evolution dynamics of infectious diseases is the mathematical representation of the mechanism of transmission of the contagion. Models with a finite number of subpopulations can be described via systems of…
We consider a system of two reaction-diffusion-advection equations describing the one dimensional directed motion of particles with superimposed diffusion and mutual alignment. For this system we show the existence of traveling wave…
This paper establishes existence, uniqueness, and an L^1-comparison principle for weak solutions of a PDE system modeling phase transition reaction-diffusion in congested crowd motion. We consider a general reaction term and mixed…
An integro-differential equation on a tree graph is used to model the evolution and spatial distribution of a population of organisms in a river network. Individual organisms become mobile at a constant rate, and disperse according to an…
We consider in this paper a solvable model for the motion of molecular motors. Based on the averaging principle, we reduce the problem to a diffusion process on a graph. We then calculate the effective speed of transportation of these…
We consider one-dimensional reaction-diffusion equations for a large class of spatially periodic nonlinearities (including multistable ones) and study the asymptotic behavior of solutions with Heaviside type initial data. Our analysis…
In this article we formulate new models for coupled systems of bulk-surface reaction-diffusion equations on stationary volumes. The bulk reaction-diffusion equations are coupled to the surface reaction-diffusion equations through linear…
This paper is devoted to the study of some nonlinear parabolic equations with discontinuous diffusion intensities. Such problems appear naturally in physical and biological models. Our analysis is based on variational techniques and in…