相关论文: Global Existence for some Cross Diffusion Systems …
The source term in a reaction-diffusion system, in general, does not involve explicit time dependence. A class of self-limiting growth models dealing with animal and tumor growth and bacterial population in a culture, on the other hand are…
We consider a reaction-diffusion system where some components react and diffuse on the boundary of a region, while other components diffuse in the interior and react with those on the boundary through mass transport. We establish criteria…
Patterns in reaction-diffusion systems near primary bifurcations can be studied locally and classified by means of amplitude equations. This is not possible for excitable reaction-diffusion systems. In this Letter we propose a global…
Reaction-diffusion processes are the foundational model for a diverse range of complex systems, ranging from biochemical reactions to social agent-based phenomena. The underlying dynamics of these systems occur at the individual…
We establish certain maximum principles for a class of strongly coupled elliptic (or cross diffusion) systems of $m\ge2$ equations. The reaction parts can be non cooperative. These new results will be crucial in obtaining coexistence and…
A finite-volume scheme for a cross-diffusion model arising from the mean-field limit of an interacting particle system for multiple population species is studied. The existence of discrete solutions and a discrete entropy production…
We investigate a class of three-component reaction-diffusion systems subject to mass control and a newly introduced structural assumption, referred to as linear intermediate weighted sum condition. Under these hypotheses, we establish the…
We propose the deterministic rate equation of three-species in the reaction - diffusion system. For this case, our purpose is to carry out the decay process in our three-species reaction-diffusion model of the form $A+B+C\to D$. The…
General conditions are established under which reaction-cross-diffusion systems can undergo spatiotemporal pattern-forming instabilities. Recent work has focused on designing systems theoretically and experimentally to exhibit patterns with…
We study a one-dimensional cross-diffusion system for two interacting populations on the torus, with a linear pressure law and different mobilities. For arbitrary bounded non-negative initial data, we show that any good approximation…
We propose and analyze a one-dimensional multi-species cross-diffusion system with non-zero-flux boundary conditions on a moving domain, motivated by the mod- eling of a Physical Vapor Deposition process. Using the boundedness by entropy…
The global existence of renormalised solutions and convergence to equilibrium for reaction-diffusion systems with non-linear diffusion are investigated. The system is assumed to have quasi-positive non-linearities and to satisfy an entropy…
We revisit a classical continuum model for the diffusion of multiple species with size-exclusion constraint, which leads to a degenerate nonlinear cross-diffusion system. The purpose of this article is twofold: first, it aims at a…
The species-area relationship is one of the central generalizations in ecology however its origin has remained a puzzle. Since ecosystems are understood as energy transduction systems, the regularities in species richness are considered to…
Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…
We look for similarity transformations which yield mappings between different one-dimensional reaction-diffusion processes. In this way results obtained for special systems can be generalized to equivalent reaction-diffusion models. The…
In this paper, we prove global-in-time existence of strong solutions to a class of fractional parabolic reaction-diffusion systems posed in a bounded domain of $\mathbb{R}^N$. The nonlinear reactive terms are assumed to satisfy natural…
We rigorously prove the passage from a Lotka-Volterra reaction-diffusion system towards a cross-diffusion system at the fast reaction limit. The system models a competition of two species, where one species has a more diverse diet than the…
We treat a model of population dynamics in a periodic environment presenting a fast diffusion line. This phenomenon is modelled via a "road-field" system, which is a system of coupled reaction-diffusion equations set in domains of different…
Reaction-diffusion models have been used over decades to study biological systems. In this context, evolution equations for probability distribution functions and the associated stochastic differential equations have nowadays become…