相关论文: Existence and qualitative properties of kinetic fu…

We shall study special regularity properties of solutions to some nonlinear dispersive models. The goal is to show how regularity on the initial data is transferred to the solutions. This will depend on the spaces where regularity is…

Hall-MHD is a mixed hyperbolic-parabolic partial differential equation that describes the dynamics of an ideal two fluid plasma with massless electrons. We study the only shock wave family that exists in this system (the other…

In this paper we investigate stability of travelling wave solutions to a class of reaction-diffusion equations perturbed by infinite-dimensional additive noise with H\"older continuous paths, covering in particular fractional Brownian…

Motivated by the work of D. Hoff and K. Zumbrun (Indiana Univ. Math. J. 44: 603-676, 1995), we investigate the diffusion wave phenomena in three-dimensional incompressible viscoelastic flows. By employing the representation formula of the…

A class of two-species ({\it three-states}) bimolecular diffusion-limited models of classical particles with hard-core reacting and diffusing in a hypercubic lattice of arbitrary dimension is investigated. The manifolds on which the…

We investigate traveling wave solutions for a nonlinear system of two coupled reaction-diffusion equations characterized by double degenerate diffusivity: \[n_t= -f(n,b), \quad b_t=[g(n)h(b)b_x]_x+f(n,b).\] These systems mainly appear in…

We consider the asymptotic behavior of perturbations of Lax and overcompressive type viscous shock profiles arising in systems of regularized conservation laws with strictly parabolic viscosity, and also in systems of conservation laws with…

In this paper we establish the orbital stability of periodic traveling waves for a general class of dispersive equations. We use the Implicit Function Theorem to guarantee the existence of smooth solutions depending of the corresponding…

The Riemann problem for the discrete conservation law $2 \dot{u}_n + u^2_{n+1} - u^2_{n-1} = 0$ is classified using Whitham modulation theory, a quasi-continuum approximation, and numerical simulations. A surprisingly elaborate set of…

This paper is concerned with the traveling waves of delayed reaction-diffusion systems where the reaction function possesses the mixed quasimonotonicity property. By the so-called monotone iteration scheme and Schauder's fixed point…

We discuss recent work on the static and dynamical properties of the asymmetric exclusion process, generalized to include the effect of disorder. We study in turn: random disorder in the properties of particles; disorder in the spatial…

We investigate the dynamic properties of elastic lattices defined by tessellations of a curved hyperbolic space. The lattices are obtained by projecting nodes of a regular hyperbolic tessellation onto a flat disk and then connecting those…

We study the properties of wave functions and the wave-packet dynamics in quasiperiodic tight-binding models in one, two, and three dimensions. The atoms in the one-dimensional quasiperiodic chains are coupled by weak and strong bonds…

Distributed-order time-fractional wave equations appear in the modeling of wave propagation in viscoelastic media. The material characteristics of the medium are modeled through constitutive functions or distributions in the…

The Dupree-Weinstock renormalization is used to prove that a reactive closure exists for drift wave turbulence in magnetized plasmas. The result is used to explain recent results in gyrokinetic simulations and is also related to the…

We analyse a generalised Fokker-Planck equation by making essential use of its linearisability through a Cole-Hopf transformation. We determine solutions of travelling wave and multi-kink type by resorting to a geometric construction in the…

This paper considers two-dimensional stratified water waves propagating under the force of gravity over an impermeable flat bed and with a free surface. We prove the existence of a global continuum of classical solutions that are periodic…

We present some analytical solutions to the Einstein equations, describing radiating collapsing spheres in the diffusion approximation. Solutions allow for modeling physical reasonable situations. The temperature is calculated for each…

A modified method of functional constraints is used to construct the exact solutions of nonlinear equations of reaction-diffusion type with delay and which are associated with variable coefficients. This study considers a most generalized…

We derive sufficient conditions for the existence of a periodic traveling wave solution to an integro-difference equation with a piecewise constant growth function exhibiting a stable period2 cycle and strong Allee effect. The mean…