Related papers: Wavefronts for a degenerate reaction-diffusion sys…
Morphogenesis is central to biology but remains largely unexplored in chemistry. Reaction-diffusion (RD) mechanisms are, however, essential to understand how shape emerges in the living world. While numerical methods confirm the incredible…
Scattering hinders the passage of light through random media and consequently limits the usefulness of optical techniques for sensing and imaging. Thus, methods for increasing the transmission of light through such random media are of…
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 a broad class of non-local advection-diffusion models describing the behaviour of an arbitrary number of interacting species, each moving in response to the non-local presence of others. Our model allows for different…
We investigate travelling wave solutions in reaction-diffusion models of animal range expansion in the case that population diffusion is density-dependent. We find that the speed of the selected wave depends critically on the strength of…
A wavefront solution for quantum (capacitively coupled) transmission lines with charge discreteness (PRB {\bf 64}, 235309 (2001)) is proposed for the first time. The nonlinearity of the system becomes deeply related to charge discreteness.…
We propose a reaction-transport model for CTRW with non-linear reactions and non-exponential waiting time distributions. We derive non-linear evolution equation for mesoscopic density of particles. We apply this equation to the problem of…
We introduce an extension of the concept of renormalised solutions for entropy-dissipating reaction-diffusion systems due to J. Fischer (Arch. Ration. Mech. Anal. 218, 2015) to systems coupled by nonlinear interface conditions. For this…
We prove the existence of a global solution to the Cauchy problem for a nonlinear reaction-diffusion system coupled with a system of ordinary differential equations. The system models the propagation of a combustion front in a porous medium…
We prove existence and uniqueness of travelling waves for a reaction-diffusion system coupling a classical reaction-diffusion equation in a strip with a diffusion equation on a line. To do this we use a continuation method which leads to…
We establish two integral variational principles for the spreading speed of the one dimensional reaction diffusion equation with Stefan boundary conditions. The first principle is valid for monostable reaction terms and the second principle…
In this work we prove global existence and uniform boundedness of solutions of 2X2 reaction-diffusion systems with control of mass structure and nonlinearities of unlimited growth. Furthermore the results are obtained without restrictions…
We are revisiting the topic of travelling fronts for the food-limited (FL) model with spatio-temporal nonlocal reaction. These solutions are crucial for understanding the whole model dynamics. Firstly, we prove the existence of monotone…
We consider combustion problems in the presence of complex chemistry and nonlinear diffusion laws leading to fully nonlinear multispecies reaction-diffusion equations. We establish results of existence of solution and maximum principle,…
It is studied the Cauchy problem for the equations of Burgers' type but with bounded dissipation flux. Such equations degenerate to hyperbolic ones as the velocity gradient tends to infinity. Thus the discontinuous solutions are permitted.…
A thorough analysis is performed to find traveling waves in a qualitative reaction-diffusion system inspired by a predator-prey model. We provide rigorous results coming from a standard local stability analysis, numerical bifurcation…
Properties of reaction zones resulting from A+B -> C type reaction-diffusion processes are investigated by analytical and numerical methods. The reagents A and B are separated initially and, in addition, there is an initial macroscopic…
This study uses a simplified detonation model to investigate the behaviour of detonations with galloping-like pulsations. The reactive Burgers equation is used for the hydrodynamic equation, coupled to a pulsed source whereby all 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…
We study the asymptotic behaviour of sharp front solutions arising from the nonlinear diffusion equation \theta_t = (D(\theta)\theta_x)_x, where the diffusivity is an exponential function D({\theta}) = D_o exp(\beta\theta). This problem…