Related papers: Large time behaviour for a nonlocal diffusion - co…

We study two initial value problems of the linear diffusion equation and a nonlinear diffusion equation, when Cauchy data are bounded and oscillate mildly. The latter nonlinear heat equation is the equation of the curvature flow, when the…

As a first step in the first passage problem for passive tracer in stratified porous media, we consider the case of a two-dimensional system consisting of two layers with different convection velocities. Using a lattice generating function…

We construct a time-asymptotic expansion with pointwise remainder estimates for solutions to 1D compressible Navier--Stokes equations. The leading-order term is the well-known diffusion wave and the higher-order terms are newly introduced…

In this article, we study the large time behavior of solutions of first-order Hamilton-Jacobi Equations, set in a bounded domain with nonlinear Neumann boundary conditions, including the case of dynamical boundary conditions. We establish…

We study an abstract family of advection-diffusion equations within the framework of the fractional Laplacian. The system involves two independent diffusion parameters: one introduced via a damping operator acting on the scalar unknown and…

We study a 1D transport equation with nonlocal velocity and show the formation of singularities in finite time for a generic family of initial data. By adding a diffusion term the finite time singularity is prevented and the solutions exist…

This paper deals with the existence, monotonicity, uniqueness and asymptotic behaviour of travelling wavefronts for a class of temporally delayed, spatially nonlocal diffusion equations.

In this article we study the long-time behavior of incompressible ideal flow in a half plane from the point of view of vortex scattering. Our main result is that certain asymptotic states for half-plane vortex dynamics decompose naturally…

In this paper we analyze the large-time behavior of weak solutions to polytropic fluid models possibly including quantum and capillary effects. Formal a priori estimates show that the density of solutions to these systems should disperse…

Small oscillations of an elastic system of point masses (particles) with a nonlocal interaction are considered. We study the asymptotic behavior of the system, when number of particles tends to infinity, and the distances between them and…

We consider two types of non linear fast diffusion equations in R^N:(1) External drift type equation with general external potential. It is a natural extension of the harmonic potential case, which has been studied in many papers. In this…

This paper investigates the asymptotic behaviour of solutions to certain infinite systems of coupled recurrence relations. In particular, we obtain a characterisation of those initial values which lead to a convergent solution, and for…

We propose a generalized diffusion equation for a flat Euclidean space subjected to a continuous infinitesimal scale transform. For the special cases of an algebraic or exponential expansion/contraction, governed by time-dependent scale…

Motivated by recent problems in mathematical cosmology, in which temporal averaging methods are applied in order to analyze the future asymptotics of models which exhibit oscillatory behavior, we provide a theorem concerning the large-time…

This paper is concerned with a diffusive Lotka-Volterra cooperative modelwith population flux by attractive transition. We study the time-global well-posedness and the large time behavior of solutions in a case where the habitat is a…

We consider a two-dimensional model of double-diffusive convection and its time discretisation using a second-order scheme which treat the nonlinear term explicitly (backward differentiation formula with a one-leg method). Uniform bounds on…

In this report we obtain higher order asymptotic expansions of solutions to wave equations with frictional and viscoelastic damping terms. Although the diffusion phenomena are dominant, differences between the solutions we deal with and…

We derive general bounds for the large time size of supnorm values of solutions to one-dimensional advection-diffusion equations with initial data in Lp0 (R) \cap L1 for some 1 <= p0 < \infty, and arbitrary bounded advection speeds b(x, t),…

We prove the large time behavior of solutions to a coupled thermo-diffusion arising in the modelling of the motion of hot colloidal particles in porous media. Additionally, we also ensure the uniqueness of solutions of the target problem.…

This paper concerns periodic solutions for a 1D-model with nonlocal velocity given by the periodic Hilbert transform. There is a rich literature showing that this model presents singular behavior of solutions via numerics and mathematical…