Related papers: Entropy methods and convergence to equilibrium for…
This paper is concerned with reaction-diffusion systems of two symmetric species in spatial dimension one, having two stable symmetric equilibria connected by a symmetric standing front. The first order variation of the speed of this front…
In this paper, we study a numerical approximation for a class of stationary states for reaction-diffusion system with m densities having disjoint support, which are governed by a minimization problem. We use quantitative properties of both…
Diffusion within porous media, such as biological tissues, exhibits departures from conventional Fick's laws, which could result in space-fractional diffusion. The paper considers a reaction-diffusion system with two spatial compartments --…
Deterministic diffusive systems such as the periodic Lorentz gas, multi-baker map, as well as spatially periodic systems of interacting particles, have non-equilibrium stationary states with fractal properties when put in contact with…
A new kinetic model is proposed where the equilibrium distribution with bounded support has a range of velocities about two average velocities in 1D. In 2D, the equilibrium distribution function has a range of velocities about four average…
A coupled system of nonlinear mixed-type equations modeling early stages of angiogenesis is analyzed in a bounded domain. The system consists of stochastic differential equations describing the movement of the positions of the tip and stalk…
In this work we study global well-posedness and large time behaviour for a typical reaction--diffusion system, which include degenerate diffusion, and whose non-linearities arise from chemical reactions. We show that there is an {\it…
A hallmark of a plethora of intracellular signaling pathways is the spatial separation of activation and deactivation processes that potentially results in precipitous gradients of activated proteins. The classical Metabolic Control…
We derive a class of multi-species aggregation-diffusion systems from stochastic interacting particle systems via relative entropy method with quantitative bounds. We show an algebraic $L^1$-convergence result using moderately interacting…
We look for similarity transformations which yield mappings between different one-dimensional reaction-diffusion processes. In this way results obtained for special systems can be generalized to equivalent reaction-diffusion models. The…
This paper is devoted to the study of systems of reaction-cross diffusion equations arising in population dynamics. New results of existence of weak solutions are presented, allowing to treat systems of two equations in which one of the…
We establish the boundedness of solutions of reaction-diffusion systems with quadratic (in fact slightly super-quadratic) reaction terms that satisfy a natural entropy dissipation property, in any space dimension N>2. This bound imply the…
In this paper we review various information-theoretic characterizations of the approach to equilibrium in biological systems. The replicator equation, evolutionary game theory, Markov processes and chemical reaction networks all describe…
Entropy production in stochastic mechanical systems is examined here with strict bounds on its rate. Stochastic mechanical systems include pure diffusions in Euclidean space or on Lie groups, as well as systems evolving on phase space for…
We consider a family of drift-diffusion-recombination systems, where the recombination of electrons and holes is facilitated by an intermediate energy-level for electrons in so-called trapped states. In particular, it has been proven in…
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…
The stochastic entropy generated during the evolution of a system interacting with an environment may be separated into three components, but only two of these have a non-negative mean. The third component of entropy production is…
Computation of entropy in liquids and liquid crystal phases is a big challenge in statistical physics. In this work, we extend the two-phase thermodynamic model (2PT) to shape anisotropic soft repulsive spherocylinders (SRSs) and report the…
In this paper we analyse a finite volume scheme for a nonlocal version of the Shigesada-Kawazaki-Teramoto (SKT) cross-diffusion system. We prove the existence of solutions to the scheme, derive qualitative properties of the solutions and…
We show that solutions of the chemical reaction-diffusion system associated to $A+B\rightleftharpoons C$ in one spatial dimension can be approximated in $L^2$ on any finite time interval by solutions of a space discretized ODE system which…