Related papers: Freezing Stochastic Travelling Waves
In this article, we study the stability of solutions to 3D stochastic primitive equations driven by fractional noise. Since the fractional Brownian motion is essentially different from Brownian motion, lots of stochastic analysis tools are…
In this paper, we consider the extended stochastic Navier-Stokes equations with Caputo derivative driven by fractional Brownian motion. We firstly derive the pathwise spatial and temporal regularity of the generalized Ornstein-Uhlenbeck…
In this paper we consider the spectral and nonlinear stability of periodic traveling wave solutions of a generalized Kuramoto-Sivashinsky equation. In particular, we resolve the long-standing question of nonlinear modulational stability by…
e study the minimal wave speed and the asymptotics of the traveling wave solutions of a competitive Lotka Volterra system. The existence of the traveling wave solutions is derived by monotone iteration. The asymptotic behaviors of the wave…
This thesis aims at investigating the first steps toward an unconditionally stable space-time isogeometric method, based on splines of maximal regularity, for the linear acoustic wave equation. The unconditional stability of space-time…
The present paper introduces stochastic velocity as improvement for moving particle semi-implicit (MPS) method. This improvement is to overcome energy loss caused by numerical dissipation in the basic MPS that brings about rapid decay of…
The FitzHugh-Nagumo equation, which was derived as a simplification of the Hodgkin-Huxley model for nerve impulse propagation, has been extensively studied as a paradigmatic activator-inhibitor system. We consider the version of this system…
We study the stability/instability of the subsonic travelling waves of the Nonlinear Schr\"odinger Equation in dimension one. Our aim is to propose several methods for showing instability (use of the Grillakis-Shatah-Strauss theory, proof…
We consider one dimensional porous media equations in spatially periodic environment. We will construct a periodic traveling sharp wave whose profile tends to a positive steady state at left infinity and takes zero on the right half line,…
We study the long-time behavior of solutions to a stochastically driven Navier-Stokes system describing the motion of a compressible viscous fluid driven by a temporal multiplicative white noise perturbation. The existence of stationary…
We consider the quartic focusing Half Wave equation (HW) in one space dimension. We show first that that there exist traveling wave solutions with arbitrary small $H^{\frac 12}(\R)$ norm. This fact shows that small data scattering is not…
We analyze the numerical solutions of a stochastic Arctic sea ice model with constant additive noise over a wide range of external heat-fluxes, $\Delta F_0$, which correspond to greenhouse gas forcing. The variability that the stochasticity…
This paper is concerned with the traveling wave solutions and asymptotic spreading of delayed lattice differential equations without quasimonotonicity. The spreading speed is obtained by constructing auxiliary equations and using the theory…
We prove the small-noise large deviation principle for the three-dimensional primitive equations with transport noise and turbulent pressure. Transport noise is important for geophysical fluid dynamics applications, as it takes into account…
We address the dynamical and statistical description of stably stratified turbulent boundary layers with the important example of the atmospheric boundary layer with a stable temperature stratification in mind. Traditional approaches to…
Analysis of the speed of propagation in parabolic operators is frequently carried out considering the minimal speed at which its traveling waves move. This value depends on the solution concept being considered. We analyze an extensive…
We consider the stability and instability of periodic travling waves for Korteweg-de Vries type equations with fractional dispersion and other nonlinear dispersive equations. We establish that a constrained minimizer for the related…
Recently, the Whitham and capillary-Whitham equations were shown to accurately model the evolution of surface waves on shallow water. In order to gain a deeper understanding of these equations, we compute periodic, traveling-wave solutions…
This paper establishes strong convergence rates for the spatial finite element discretization of a two-dimensional stochastic Navier--Stokes system with transport noise and no-slip boundary conditions on a convex polygonal domain. The main…
We consider the barotropic Navier--Stokes system driven by a physically well-motivated transport noise in both continuity as well as momentum equation. We focus on three different situations: (i) the noise is smooth in time and the…