Related papers: Front-like entire solutions for monostable reactio…
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…
This paper is concerned with analysis of coupled fractional reaction-diffusion equations. It provides analytical comparison for the fractional and regular reaction-diffusion systems. As an example, the reaction-diffusion model with cubic…
In this paper, we consider a reaction-diffusion system describing the propagation of flames under the assumption of ignition-temperature kinetics and fractional reaction order. It was shown in [3] that this system admits a traveling front…
We consider general reaction diffusion systems posed on rectangular lattices in two or more spatial dimensions. We show that travelling wave solutions to such systems that propagate in rational directions are nonlinearly stable under small…
We prove existence of transition fronts for a large class of reaction-diffusion equations in one dimension, with inhomogeneous monostable reactions. We construct these as perturbations of corresponding front-like solutions to the…
Mass-conserving reaction-diffusion systems with bistable nonlinearity are considered under general assumptions. The existence of stationary solutions with a single internal transition layer in such reaction-diffusion systems is shown using…
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…
We study the reaction-fractional-diffusion equation $u_t+(-\Delta)^{s} u=f(u)$ with ignition and monostable reactions $f$, and $s\in(0,1)$. We obtain the first optimal bounds on the propagation of front-like solutions in the cases where no…
We construct nontrivial entire solutions for a bistable reaction-diffusion equation in a class of domains that are unbounded in one direction. The motivation comes from recent results of Berestycki, Bouhours, and Chapuisat concerning…
We construct entire solutions of bistable reaction-diffusion equations by mixing finite planar fronts, which form a finite-dimensional manifold. These entire solutions are generalized traveling fronts, that is, transition fronts. We also…
This paper studies the solutions of a reaction--diffusion system with nonlinearities that generalise the Lengyel--Epstein and FitzHugh--Nagumo nonlinearities. Sufficient conditions are derived for the global asymptotic stability of the…
We consider flame front propagation in channel geometries. The steady state solution in this problem is space dependent, and therefore the linear stability analysis is described by a partial integro-differential equation with a space…
Systems consisting of a single ordinary differential equation coupled with one reaction-diffusion equation in a bounded domain and with the Neumann boundary conditions are studied in the case of particular nonlinearities from the…
Reaction-diffusion equations appear in biology and chemistry, and combine linear diffusion with different kind of reaction terms. Some of them are remarkable from the mathematical point of view, since they admit families of travelling waves…
This paper deals with front propagation dynamics of monostable equations with nonlocal dispersal in spatially periodic habitats. In the authors' earlier works, it is shown that a general spatially periodic monostable equation with nonlocal…
In this paper we study a nonlinear reaction-diffusion system which models an infectious disease caused by bacteria such as those for cholera. One of the significant features in this model is that a certain portion of the recovered human…
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…
A general system of several ordinary differential equations coupled with a reaction-diffusion equation in a bounded domain with zero-flux boundary condition is studied in the context of pattern formation. These initial-boundary value…
This paper is concerned with existence, non-existence and uniqueness of positive (coexistence) steady states to a predator-prey system with density-dependent dispersal. To overcome the analytical obstacle caused by the cross-diffusion…
In this paper, we study the existence and stability of travelling wave solutions of a kinetic reaction-transport equation. The model describes particles moving according to a velocity-jump process, and proliferating thanks to a reaction…