相关论文: On the stability of totally upwind schemes for the…

In this paper, we establish the sufficient conditions guaranteeing global uniform exponential stability, or at least global asymptotic stability, of all solutions for nonlinear dynamical systems, also known as global incremental stability…

We present a rigorous numerical proof based on interval arithmetic computations categorizing the linearized and nonlinear stability of periodic viscous roll waves of the KdV-KS equation modeling weakly unstable flow of a thin fluid film on…

We consider the motion described by the Navier-Stokes equations in a box with periodic boundary conditions. First we prove the existence of global strong two-dimensional solutions. Next we show the existence of global strong…

This report addresses the boundary value problem for a second-order linear singularly perturbed FIDE. Traditional methods for solving these equations often face stability issues when dealing with small perturbation parameters. We propose an…

We introduce a refinement of the persistence diagram, the graded persistence diagram. It is the Mobius inversion of the graded rank function, which is obtained from the rank function using the unary numeral system. Both persistence diagrams…

We extend our recent work with K. Zumbrun on long-time stability of multi-dimensional noncharacteristic viscous boundary layers of a class of symmetrizable hyperbolic-parabolic systems. Our main improvements are (i) to establish the…

We consider in this paper a numerical approximation of Poisson-Nernst-Planck-Navier- Stokes (PNP-NS) system. We construct a decoupled semi-discrete and fully discrete scheme that enjoys the properties of positivity preserving, mass…

In this note we propose the exact artificial boundary conditions formula to the fractional reaction-subdiffusion equation on an unbounded domain. With the application of Laplace transformation, the exact artificial boundary conditions…

We improve the preceding results obtained by the first and the second authors in [3]. They concern the stability issue of the inverse problem that consists in determining the potential and the damping coefficient in a wave equation from an…

Optimal error estimates of stable and stabilized Lagrange-Galerkin (LG) schemes for natural convection problems are proved under a mild condition on time increment and mesh size. The schemes maintain the common advantages of the LG method,…

We present well-balanced, high-order, semi-discrete numerical schemes for one-dimensional blood flow models with discontinuous mechanical properties and algebraic source terms representing friction and gravity. While discontinuities in…

This work presents a novel stabilization strategy for the Galerkin formulation of the incompressible Navier-Stokes equations, developed to achieve high accuracy while ensuring convergence and compatibility with high-order elements on…

We apply the local discontinuous Galerkin (LDG for short) method to solve a mixed boundary value problems for the Helmholtz equation in bounded polygonal domain in 2D. Under some assumptions on regularity of the solution of an adjoint…

This paper is concerned with the existence, uniqueness and nonlinear stability of stationary solutions to the Cauchy problem of the full compressible Navier-Stokes-Korteweg system effected by external force of general form in…

This paper studies the boundary value problem on the steady compressible Navier-Stokes-Fourier system in a channel domain $(0,1)\times\mathbb{T}^2$ with a class of generalized slip boundary conditions that were systematically derived from…

This paper concerns the inverse source problems for the time-harmonic elastic and electromagnetic wave equations. The goal is to determine the external force and the electric current density from boundary measurements of the radiated wave…

This paper is concerned with the initial-boundary value problem for the Einstein equations in a first-order generalized harmonic formulation. We impose boundary conditions that preserve the constraints and control the incoming gravitational…

In this paper, we are interested in constructing a scheme solving compressible Navier--Stokes equations, with desired properties including high order spatial accuracy, conservation, and positivity-preserving of density and internal energy…

In this paper, the one-dimensional compressible Navier-Stokes system with outer pressure boundary conditions is investigated. Under some suitable assumptions, we prove that the specific volume and the temperature are bounded from below and…

This paper presents the linear global stability analysis of the incompressible axisymmetric boundary layer on a circular cylinder. The base flow is parallel to the axis of the cylinder at inlet. The pressure gradient is zero in the…