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This paper is devoted to the study of some qualitative and quantitative aspects of nonlinear propagation phenomena in diffusive media. More precisely, we consider the case a reaction-diffusion equation in a periodic medium with…

Analysis of PDEs · Mathematics 2009-04-27 Francois Hamel , Yannick Sire

In this work, we investigate a reaction-diffusion system in which both species are influenced by self-diffusion. Due to Hopf's boundary lemma, we obtain the boundedness of the classical solution of the system. By considering a particular…

Analysis of PDEs · Mathematics 2024-04-22 Ningning Zhu , Dongpo Hu , Huili Bi

Reaction-diffusion equations are studied on bounded, time-periodic domains with zero Dirichlet boundary conditions. The long-time behaviour is shown to depend on the principal periodic eigenvalue of a transformed periodic-parabolic problem.…

Analysis of PDEs · Mathematics 2023-07-18 Jane Allwright

Dynamic phenomena in social and biological sciences can often be modeled by employing reaction-diffusion equations. When addressing the control of these modes, from a mathematical viewpoint one of the main challenges is that, because of the…

Optimization and Control · Mathematics 2020-06-02 Domènec Ruiz-Balet , Enrique Zuazua

We consider reaction diffusion systems where components diffuse inside the domain and react on the surface through mass transport type boundary conditions. Under reasonable hypotheses, we establish the existence of component wise…

Analysis of PDEs · Mathematics 2020-05-05 Vandana Sharma

Second initial boundary problem in narrow domains of width $\epsilon\ll 1$ for linear second order differential equations with nonlinear boundary conditions is considered in this paper. Using probabilistic methods we show that the solution…

Probability · Mathematics 2010-11-30 Mark Freidlin , Konstantinos Spiliopoulos

We have studied the front propagation in a one dimensional case of combustion by solving numerically an advection-reaction-diffusion equation. The physical model is simplified so that no coupling phenomena are considered and the reacting…

Fluid Dynamics · Physics 2011-04-07 Federico Bianco , Sergio Chibbaro , Roger Prud'homme

The dynamics of a coupled two-component nonequilibrium system is examined by means of continuum field theory representing the corresponding master equation. Particles of species A may perform hopping processes only when particles of…

Statistical Mechanics · Physics 2009-10-31 S. Trimper , U. C. Taeuber , G. M. Schuetz

We study a reaction-diffusion-convection problem with nonlinear drift posed in a domain with periodically arranged obstacles. The non-linearity in the drift is linked to the hydrodynamic limit of a totally asymmetric simple exclusion…

Analysis of PDEs · Mathematics 2022-04-05 Vishnu Raveendran , Emilio N. M. Cirillo , Adrian Muntean

Realistic examples of reaction-diffusion phenomena governing spatial and spatiotemporal pattern formation are rarely isolated systems, either chemically or thermodynamically. However, even formulations of `open' reaction-diffusion systems…

Pattern Formation and Solitons · Physics 2021-05-14 Andrew L. Krause , Václav Klika , Philip K. Maini , Denis Headon , Eamonn A. Gaffney

A one-component bistable reaction-diffusion system with asymmetric nonlocal coup ling is derived as limiting case of a two-component activator-inhibitor reaction -diffusion model with differential advection. The effects of asymmetric…

Pattern Formation and Solitons · Physics 2014-05-20 Julien Siebert , Sergio Alonso , Markus Bär , Eckehard Schöll

A general reaction-diffusion equation with spatiotemporal delay and homogeneous Dirichlet boundary condition is considered. The existence and stability of positive steady state solutions are proved via studying an equivalent…

Analysis of PDEs · Mathematics 2021-02-24 Wenjie Zuo , Junping Shi

Understanding the asymptotic behavior of reaction-diffusion (RD) systems is crucial for modeling processes ranging from species coexistence in ecology to biochemical interactions within cells. In this work, we analyze RD systems in which…

Dynamical Systems · Mathematics 2025-02-18 Carlos Barajas , Jean-Jacques Slotine , Domitilla Del Vecchio

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…

Statistical Mechanics · Physics 2018-10-09 C. Escudero , S. B. Yuste , E. Abad , F. Le Vot

In many biological situations, a species arriving from a remote source diffuses in a domain confined between two parallel surfaces until it finds a binding partner. Since such a geometric shape falls in between two- and three-dimensional…

Chemical Physics · Physics 2019-11-05 Denis S. Grebenkov , Diego Krapf

We study existence and uniqueness of travelling fronts, and asymptotic speed of propagation for a non local reaction diffusion equation with spatial and genetic trait structure.

Analysis of PDEs · Mathematics 2014-12-23 Henri Berestycki , Tianling Jin , Luis Silvestre

An asymptotic equation of motion for the pattern interface in the domain-forming reaction-diffusion systems is derived. The free boundary problem is reduced to the universal equation of non-local contour dynamics in two dimensions in the…

patt-sol · Physics 2009-10-30 C. B. Muratov

We study a two-component reaction-diffusion system in which one of the reaction terms becomes singularly large. Assuming that the initial data are nonnegative and mutually segregated, we prove that the solution converges to that of the heat…

Analysis of PDEs · Mathematics 2025-06-12 Yuki Tsukamoto

We study the velocity of travelling waves of a reaction-diffusion system coupling a standard reaction-diffusion equation in a strip with a one-dimensional diffusion equation on a line. We show that it grows like the square root of the…

Analysis of PDEs · Mathematics 2015-07-02 Laurent Dietrich

The trend to equilibrium for reaction-diffusion systems modelling chemical reaction networks is investigated, in the case when reaction processes happen on subsets of the domain. We prove the convergence to equilibrium by directly showing…

Analysis of PDEs · Mathematics 2024-12-17 Laurent Desvillettes , Kim Dang Phung , Bao Quoc Tang