相关论文: Exponential decay toward equilibrium via log conve…

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…

We study metastability for symbolic dynamic. We prove that for a global system given by two independent sub-systems linked by a hole, and for a Lipschitz continuous potential, the global equilibrium state converges, as the hole shrinks, to…

We study the asymptotic behaviour of a real-valued diffusion whose non-regular drift is given as a sum of a dissipative term and a bounded measurable one. We prove that two trajectories of that diffusion converge a.s. to one another at an…

In this paper we study time semi-discrete approximations of a class of exponentially stable infinite dimensional systems with unbounded feedbacks. It has recently been proved that for time semi-discrete systems, due to high frequency…

We study the Einstein relation between diffusion and response to an external field in systems showing superdiffusion. In particular, we investigate a continuous time Levy walk where the velocity remains constant for a time \tau, with…

We investigate the occurrence of exponential relaxation in a certain class of closed, finite systems on the basis of a time-convolutionless (TCL) projection operator expansion for a specific class of initial states with vanishing…

In this paper, we consider a class of infinitely degenerate partial differential systems to obtain the Nash equilibria in the mean field games. The degeneracy in the diffusion and the Hamiltonian may be different. This feature brings…

We consider the spatially homogeneous Boltzmann equation for inelastic hard spheres (with constant restitution coefficient $\alpha \in (0,1)$) under the thermalization induced by a host medium with a fixed Maxwellian distribution. We prove…

We introduce non-linear diffusion in a classical diffusion advection model with non local aggregative coupling on the circle, that exhibits a transition from an uncoherent state to a coherent one when the coupling strength is increased. We…

We consider the Cauchy problem for a system of balance laws derived from a chemotaxis model with singular sensitivity in multiple space dimensions. Utilizing energy methods, we first prove the global well-posedness of classical solutions to…

Reaction-diffusion systems with mass dissipation are known to possess blow-up solutions in high dimensions when the nonlinearities have super quadratic growth rates. In dimension one, it has been shown recently that one can have global…

We study repeated games where players use an exponential learning scheme in order to adapt to an ever-changing environment. If the game's payoffs are subject to random perturbations, this scheme leads to a new stochastic version of the…

This paper presents new analytical results for a class of nonlinear parabolic systems of partial different equations with small cross-diffusion which describe the macroscopic dynamics of a variety of large systems of interacting particles.…

We consider a class of mechanical particle systems with deterministic particle-disk interactions coupled to Gibbs heat reservoirs at possibly different temperatures. We show that there exists a unique (non-equilibrium) steady state. This…

We conjecture that for a wide class of interacting particle systems evolving in discrete time, namely conservative cellular automata with piecewise linear flow diagram, relaxation to the limit set follows the same power law at critical…

In this work we investigate the rate of convergence to equilibrium for subcritical solutions to the Becker-D\"oring equations with physically relevant coagulation and fragmentation coefficients and mild assumptions on the given initial…

We consider a spatially homogeneous advection-diffusion equation in which the diffusion tensor and drift velocity are time-independent, but otherwise general. We derive asymptotic expressions, valid at large distances from a steady point…

We consider random dynamical systems on manifolds modeled by a skew product which have certain geometric properties and whose measures satisfy quenched decay of correlations at a sufficient rate. We prove that the limiting distribution for…

Chemical reaction networks in living cells maintain precise control over thousands of metabolites despite operating far from equilibrium under constant perturbations. While mass action kinetics accurately describe the underlying dynamics,…

We consider solvability of the generalized reaction-diffusion equation with both space- and time-dependent diffusion and reaction terms by means of the similarity method. By introducing the similarity variable, the reaction-diffusion…