Related papers: Nonlinear reaction-diffusion systems with a non-co…
This paper addresses the derivation of generic and tractable sufficient conditions ensuring the stability of a coupled system composed of a reaction-diffusion partial differential equation (PDE) and a finite-dimensional linear time…
Solitons, defined as nonlinear waves which can reflect from boundaries or transmit through each other, are found in conservative, fully integrable systems. Similar phenomena, dubbed quasi-solitons, have been observed also in dissipative,…
In this paper, we study unique, globally defined uniformly bounded weak solutions for a class of semilinear reaction-diffusion-advection systems. The coefficients of the differential operators and the initial data are only required to be…
In this paper, we investigate multidimensional first-order quasi-linear systems and find necessary conditions for them to admit Hamiltonian formulation. The insufficiency of the conditions is related to the Poisson cohomology of the…
We study diffusion-controlled processes in nonequilibrium steady states, where standard rate theory assumptions break down. Using transition path theory, we generalize the relations between reactive probability fluxes and measures of the…
We investigate a nonlinear parabolic reaction-diffusion equation describing the oxygen concentration in encapsulated pancreatic cells with a general core-shell geometry. This geometry introduces a discontinuous diffusion coefficient as the…
In this paper, a class of reaction-diffusion equations for Multiple Sclerosis is presented. These models are derived by means of a diffusive limit starting from a proper kinetic description, taking account of the underlying microscopic…
This note shows how classical tools from linear control theory can be leveraged to provide a global analysis of nonlinear reaction-diffusion models. The approach is differential in nature. It proceeds from classical tools of contraction…
In this paper, we propose a new mathematical model nonlinear reaction-diffusion PDE's describing the dynamics of propagation of cancer. Here the mixed problem for the proposed PDE's is investigated and by applying obtained results…
The shadow limit is a versatile tool used to study the reduction of reaction-diffusion systems into simpler PDE-ODE models by letting one of the diffusion coefficients tend to infinity. This reduction has been used to understand different…
The master equation describing non-equilibrium one-dimensional problems like diffusion limited reactions or critical dynamics of classical spin systems can be written as a Schr\"odinger equation in which the wave function is the probability…
This paper investigates a class of novel nonlinear reaction-diffusion systems that couple forward-backward with fractional diffusion for image restoration, offering the advantage of preserving both contour features and textures. The…
Symmetries and adjoint-symmetries are two fundamental (coordinate-free) structures of PDE systems. Recent work has developed several new algebraic aspects of adjoint-symmetries: three fundamental actions of symmetries on adjoint-symmetries;…
We present global existence results for solutions of reaction-diffusion systems on evolving domains. Global existence results for a class of reaction-diffusion systems on fixed domains are extended to the same systems posed on spatially…
A system of equations of the reaction-diffusion type is studied in the framework of both the direct and the inverse prolongation structure. We find that this system allows an incomplete prolongation Lie algebra, which is used to find the…
We consider a single species reaction diffusion system on a two dimensional lattice where the particles $A$ are biased to move towards their nearest neighbours and annihilate as they meet; $A + A \to \emptyset$. Allowing the bias to take…
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…
We consider two-component nonlinear dissipative spatially extended systems of reaction-cross-diffusion type. Previously, such systems were shown to support "quasi-soliton" pulses, which have fixed stable structure but can reflect from…
Using a matrix product method the steady-state of a family of disordered reaction-diffusion systems consisting of different species of interacting classical particles moving on a lattice with periodic boundary conditions is studied. A new…
This paper demonstrates a lower and upper solution method to investigate the asymptotic behaviour of the conservative reaction-diffusion systems associated with Markovian process algebra models. In particular, we have proved the uniform…