相关论文: BV instability for the Lax-Friedrichs scheme
We investigate $L^2$-contraction and time-asymptotic stability of large shock for scalar viscous conservation laws with polynomial flux. For the strictly convex flux $f(u)=u^p $ with $2\leq p \leq 4$, we can prove $L^2$-contraction and…
Various classes of stable finite difference schemes can be constructed to obtain a numerical solution. It is important to select among all stable schemes such a scheme that is optimal in terms of certain additional criteria. In this study,…
In order to understand the nonlinear stability of many types of time-periodic travelling waves on unbounded domains, one must overcome two main difficulties: the presence of embedded neutral eigenvalues and the time-dependence of the…
Exponential stabilizability of the incompressible Navier-Stokes equations under dynamic slip boundary conditions toward arbitrary time-dependent trajectories is proven. The feedback control law is constructed explicitly using oblique…
The author presented a stochastic and variational approach to the Lax-Friedrichs finite difference scheme applied to hyperbolic scalar conservation laws and the corresponding Hamilton-Jacobi equations with convex and superlinear…
A bifurcating system subject to multiplicative noise can exhibit on-off intermittency close to the instability threshold. For a canonical system, we discuss the dependence of this intermittency on the Power Spectrum Density (PSD) of the…
We develop a stability theory for two-dimensional periodic traveling waves of general parabolic systems, possibly including conservation laws. In particular, we identify a diffusive spectral stability assumption and prove that it implies…
A compressible viscous-dispersive Euler system in one space dimension in the context of quantum hydrodynamics is considered. The dispersive term is due to quantum effects described through the Bohm potential and the viscosity term is of…
Turing patterns on unbounded domains have been widely studied in systems of reaction-diffusion equations. However, up to now, they have not been studied for systems of conservation laws. Here, we (i) derive conditions for Turing instability…
This paper derives a somewhat surprising but interesting enough result on the stabilizability of discrete-time parameterized uncertain systems. Contrary to an intuition, it shows that the growth rate of a discrete-time stabilizable system…
This paper investigates the long time stability behavior of multiphysics flow problems, namely the Navier-Stokes equations, natural convection and double-diffusive convection equations with an extrapolated blended BDF time-stepping scheme.…
We revisit the classical stability versus accuracy dilemma for the lattice Boltzmann methods (LBM). Our goal is a stable method of second-order accuracy for fluid dynamics based on the lattice Bhatnager--Gross--Krook method (LBGK). The LBGK…
Fourth-order accurate compact schemes for variable coefficient convection diffusion equations are considered. A sufficient condition for the stability of the fully discrete problem is derived using a difference equation based approach. The…
This work is concerned with the stability properties of linear stochastic differential equations with random (drift and diffusion) coefficient matrices, and the stability of a corresponding random transition matrix (or exponential…
Given the significance of physical measures in understanding the complexity of dynamical systems as well as the noisy nature of real-world systems, investigating the stability of physical measures under noise perturbations is undoubtedly a…
Particles in turbulence live complicated lives. It is nonetheless sometimes possible to find order in this complexity. It was proposed in [Falkovich et al., Phys. Rev. Lett. 110, 214502 (2013)] that pairs of Lagrangian tracers at small…
Numerical analysis for linear constant-coefficients Finite Difference schemes was developed approximately fifty years ago. It relies on the assumption of scheme stability and in particular -- for the $L^2$ setting -- on the absence of…
We present in this paper a pressure correction scheme for barotropic compressible Navier-Stokes equations, which enjoys an unconditional stability property, in the sense that the energy and maximum-principle-based a priori estimates of the…
The class of $2\times 2$ nonlinear hyperbolic systems with one genuinely nonlinear field and one linearly degenerate field are considered. Existence of global weak solutions for small initial data in fractional BV spaces $BV^s$ is proved.…
The dynamical behavior of switched affine systems is known to be more intricate than that of the well-studied switched linear systems, essentially due to the existence of distinct equilibrium points for each subsystem. First, under…