相关论文: Parametrization of Cosserat Equations

In H\"ormander inner product spaces, we investigate initial-boundary value problems for an arbitrary second order parabolic partial differential equation and the Dirichlet or a general first-order boundary conditions. We prove that the…

A choice of first-order variables for the characteristic problem of the linearized Einstein equations is found which casts the system into manifestly well-posed form. The concept of well-posedness for characteristic problems invoked is that…

We present a systematic introduction to first-order optimality conditions for mathematical programs with equilibrium constraints (MPECs), emphasizing the limitations of classical nonlinear programming techniques. The goal is twofold. First,…

We introduce a class of singular partial differential equations, the second-order hyperbolic Fuchsian systems, and we investigate the associated initial value problem when data are imposed on the singularity. First of all, we analyze a…

Given a set of response observations for a parametrized dynamical system, we seek a parametrized dynamical model that will yield uniformly small response error over a range of parameter values yet has low order. Frequently, access to…

The paper studies coincidence points of parameterized set-valued mappings (multifunctions), which provide an extended framework to cover several important topics in variational analysis and optimization that include the existence of…

It was shown recently that the constraints on the initial data for Einstein's equations may be posed as an evolutionary problem [9]. In one of the proposed two methods the constraints can be replaced by a first order symmetrizable…

We consider the problem of performing the preliminary "symmetry classification'' of a class of quasi-linear PDE's containing one or more arbitrary functions: we provide an easy condition involving these functions in order that nontrivial…

The transition between the two phases of 4D Euclidean Dynamical Triangulation [1] was long believed to be of second order until in 1996 first order behavior was found for sufficiently large systems [5,9]. However, one may wonder if this…

Second-order formulations of the 3+1 Einstein equations obtained by eliminating the extrinsic curvature in terms of the time derivative of the metric are examined with the aim of establishing whether they are well posed, in cases of…

First-order energy dissipative schemes in time are available in literature for the Poisson-Nernst-Planck (PNP) equations, but second-order ones are still in lack. This work proposes novel second-order discretization in time and finite…

Seamless global parametrization of surfaces is a key operation in geometry processing, e.g. for high-quality quad mesh generation. A common approach is to prescribe the parametric domain structure, in particular the locations of…

In Einstein theory of gravity the initial configuration of metric field and its time derivative are related to matter configuration by four equations called constraints. We use the method of conformal metrics (York Method) to solve…

The constraint equations for smooth $[n+1]$-dimensional (with $n\geq 3$) Riemannian or Lorentzian spaces satisfying the Einstein field equations are considered. It is shown, regardless of the signature of the primary space, that the…

A parameter estimation problem is considered for a linear stochastic hyperbolic equation driven by additive space-time Gaussian white noise. The damping/amplification operator is allowed to be unbounded. The estimator is of spectral type…

We prove a number of \textit{a priori} estimates for weak solutions of elliptic equations or systems with vertically independent coefficients in the upper-half space. These estimates are designed towards applications to boundary value…

Second order Sobolev metrics on the space of regular unparametrized planar curves have several desirable completeness properties not present in lower order metrics, but numerics are still largely missing. In this paper, we present…

In recent years, the success of deep learning has inspired many researchers to study the optimization of general smooth non-convex functions. However, recent works have established pessimistic worst-case complexities for this class…

We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role. Attempts have previously been made to write a second order system consisting of…

We consider the variational discretization of a linear-quadratic optimal control problem with pointwise control and state constraints. In order to allow for a Fr\'echet smooth norm, the problem is reformulated by means of a reflexive…