Related papers: Group classification of systems of non-linear reac…
In this paper, we present an approach to characterising fast-reaction limits of systems with nonlinear diffusion, when there are either two reaction-diffusion equations, or one reaction-diffusion equation and one ordinary differential…
The theory of group classification of differential equations is analyzed, substantially extended and enhanced based on the new notions of conditional equivalence group and normalized class of differential equations. Effective new techniques…
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…
Biological, physical, medical, and numerical applications involving membrane problems on different scales are numerous. We propose an extension of the standard Turing theory to the case of two domains separated by a permeable membrane. To…
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…
Modern analyses of diffusion processes have proposed nonlinear versions of the Fokker-Planck equation to account for non-classical diffusion. These nonlinear equations are usually constructed on a phenomenological basis. Here we introduce a…
The macroscopic behavior of the solution of a coupled system of partial differential equations arising in the modeling of reaction-diffusion processes in periodic porous media is analyzed. Our mathematical model can be used for studying…
We introduce the mathematical theory of the particle systems that interact via permutations, where the transition rates are assigned not to the jumps from a site to a site, but to the permutations themselves. This permutation processes can…
We review generalized Fluctuation-Dissipation Relations which are valid under general conditions even in ``non-standard systems'', e.g. out of equilibrium and/or without a Hamiltonian structure. The response functions can be expressed in…
This is the second part of the series of papers on symmetry properties of a class of variable coefficient (1+1)-dimensional nonlinear diffusion-convection equations of general form $f(x)u_t=(g(x)A(u)u_x)_x+h(x)B(u)u_x$. At first, we review…
Weakly nonlinear amplitude equations are derived for the onset of spatially extended patterns on a general class of n-component bulk-surface reaction-diffusion systems in a ball, under the assumption of linear kinetics in the bulk and…
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 present a systematic formulation of scattering theory for nonlinear interactions in one dimension and develop a nonlinear generalization of the transfer matrix that has a composition property similar to its linear analog's. We offer…
We show that the Turing patterns in reaction systems with subdiffusion can be replicated in an effective system with Markovian cross-diffusion. The effective system has the same Turing instability as the original system, and the same…
In this work we investigate the process of pattern formation in a two dimensional domain for a reaction-diffusion system with nonlinear diffusion terms and the competitive Lotka-Volterra kinetics. The linear stability analysis shows that…
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 work presents the Second-Order Sensitivity Analysis Methodology (2nd-ASAM) for nonlinear systems. This methodology yields exactly and efficiently the second-order functional derivatives of system responses (associated with physical,…
This paper proposes the Ricci-flow equation from Riemannian geometry as a general geometric framework for various nonlinear reaction-diffusion systems (and related dissipative solitons) in mathematical biology. More precisely, we propose a…
Hyperbolic reaction-diffusion equations have recently attracted attention both for their application to a variety of biological and chemical phenomena, and for their distinct features in terms of propagation speed and novel instabilities…
A system of two cubic reaction-diffusion equations for two independent gene frequencies arising in population dynamics is studied. Depending on values of coefficients, all possible Lie and $Q$-conditional (nonclassical) symmetries are…