相关论文: On the Theoretical Foundation of Overset Grid Meth…

We show that even though the Discontinuous Galerkin Spectral Element Method is stable for hyperbolic boundary-value problems, and the overset domain problem is well-posed in an appropriate norm, the energy of the approximation of the latter…

We derive entropy conserving and entropy dissipative overlapping domain formulations for systems of nonlinear hyperbolic equations in conservation form, such as would be approximated by overset mesh methods. The entropy conserving…

These lecture notes accompany two classes given at the NRHEP2 school. In the first lecture I introduce the basic concepts used for analyzing well-posedness, that is the existence of a unique solution depending continuously on given data, of…

Motivated by an analysis on the well-posedness of the initial boundary value problem for the motion of an inextensible hanging string, we first consider an initial boundary value problem for one-dimensional degenerate hyperbolic systems…

In this paper, the well-posedness is studied for the initial boundary value problem of the two-dimensional compressible ideal magnetohydrodynamic (MHD) equations in bounded perfectly conducting domains with corners. The presence of corners…

We consider the well-posedness of a class of hyperbolic partial differential equations on a one dimensional spatial domain. This class includes in particular infinite-dimensional networks of transport, wave and beam equations, or even…

The goal of this paper is to study global well-posedness, cone of dependence and loss of regularity of the solutions to a class of strictly hyperbolic equations with coefficients displaying "mild" blow-up of sublogarithmic order - $|\ln…

In this paper, complex Ginzburg-Landau (CGL) equations with superlinear growth terms are studied. We discuss the local well-posedness in the energy space H1 for the initial-boundary value problem of the equations in general domains. The…

We consider a mixed dimensional elliptic partial differential equation posed in a bulk domain with a large number of embedded interfaces. In particular, we study well-posedness of the problem and regularity of the solution. We also propose…

In this paper, we consider the well-posedness of the Cauchy problem for a physical model of the extrusion process, which is described by two systems of conservation laws with a free boundary. By suitable change of coordinates and fixed…

We derive well-posed boundary conditions for the linearized Serre equations in one spatial dimension by utilizing the energy method. An energy stable and conservative discontinuous Galerkin spectral element method with simple upwind…

This paper focuses on the 2D compressible magnetohydrodynamic (MHD) equations without magnetic diffusion in a periodic domain. We present a systematic approach to establishing the global existence of smooth solutions when the initial data…

This series of papers is devoted to the formulation and the approximation of coupling problems for nonlinear hyperbolic equations. The coupling across an interface in the physical space is formulated in term of an augmented system of…

We study hyperbolic systems of one-dimensional partial differential equations under general, possibly non-local boundary conditions. A large class of evolution equations, either on individual 1-dimensional intervals or on general networks,…

We consider a coupled system of Maxwell's equations and the equations of elasticity, which is commonly used to model piezo-electric material behavior. The boundary influence is encoded as a separate dynamics on the boundary data spaces…

There is a tendency to write the equations of general relativity as a first order symmetric system of time dependent partial differential equations. However, for numerical reasons, it might be advantageous to use a second order formulation…

The goal of this paper is to establish a global well-posedness for a broad class of strictly hyperbolic Cauchy problems with coefficients in $C^2((0,T];C^\infty(\mathbb{R}^n))$ growing polynomially in $x$ and singular in $t$. The problems…

The theory of weak solutions for nonlinear conservation laws is now well developed in the case of scalar equations [3] and for one-dimensional hyperbolic systems [1, 2]. For systems in several space dimensions, however, even the global…

In recent work, we used pseudo-differential theory to establish conditions that the initial-boundary value problem for second order systems of wave equations be strongly well-posed in a generalized sense. The applications included the…

We study the well-posedness theory for the linearized free boundary problem of incompressible ideal magnetohydrodynamics equations in a bounded domain. We express the magnetic field in terms of the velocity field and the deformation tensors…