相关论文: Lasry-Lions approximations for discounted Hamilton…

We investigate the large-time behavior of viscosity solutions of quasi-monotone weakly coupled systems of Hamilton--Jacobi equations on the $n$-dimensional torus. We establish a convergence result to asymptotic solutions as time goes to…

Low-rank tensor approximation techniques attempt to mitigate the overwhelming complexity of linear algebra tasks arising from high-dimensional applications. In this work, we study the low-rank approximability of solutions to linear systems…

We extend the geometric Hamilton-Jacobi formalism for hamiltonian mechanics to higher order field theories with regular lagrangian density. We also investigate the dependence of the formalism on the lagrangian density in the class of those…

Hamilton-Jacobi equation for Brans-Dicke theory is solved by using a long-wavelength approximation. We examine the non-linear evolution of the inhomogeneities in the dust fluid case and the cosmological constant case. In the case of dust…

We investigate training and using Gaussian kernel SVMs by approximating the kernel with an explicit finite- dimensional polynomial feature representation based on the Taylor expansion of the exponential. Although not as efficient as the…

We study existence, uniqueness and regularity properties of classical solutions to viscous Hamilton-Jacobi equations with Caputo time-fractional derivative. Our study relies on a combination of a gradient bound for the time-fractional…

It is shown that in the weak field approximation solutions of Brans-Dicke equations are simply related to the solutions of General Relativity equations for the same matter distribution. A simple method is developed which permits to obtain…

In this paper, a class of high order numerical schemes is proposed for solving Hamilton-Jacobi (H-J) equations. This work is regarded as an extension of our previous work for nonlinear degenerate parabolic equations, see Christlieb et al.…

We present an abstract framework for analyzing the weak error of fully discrete approximation schemes for linear evolution equations driven by additive Gaussian noise. First, an abstract representation formula is derived for sufficiently…

The aim of this paper is to develop a general method for constructing approximation schemes for viscosity solutions of fully nonlinear pathwise stochastic partial differential equations, and for proving their convergence. Our results apply…

This article is about both approximation theory and the numerical solution of partial differential equations (PDEs). First we introduce the notion of {\em reciprocal-log} or {\em log-lightning approximation} of analytic functions with…

In this article, we study the large time behavior of solutions of first-order Hamilton-Jacobi Equations, set in a bounded domain with nonlinear Neumann boundary conditions, including the case of dynamical boundary conditions. We establish…

We prove differentiability of the effective Lagrangian for continuous time multidimensional directed variational problems in random dynamic environments with positive dependence range in time. This implies that limiting fundamental…

The link between the treatments of constrained systems with fractional derivatives by using both Hamiltonian and Lagrangian formulations is studied. It is shown that both treatments for systems with linear velocities are equivalent.

We study discounted Hamilton Jacobi equations on networks, without putting any restriction on their geometry. Assuming the Hamiltonians continuous and coercive, we establish a comparison principle and provide representation formulae for…

The critical value of an eikonal equation is the unique value of a parameter for which the equation admits solutions and is deeply related to the effective Hamiltonian of a corresponding homogenization problem. We study approximation…

We study the representation formulae for the fundamental solutions and viscosity solutions of the Hamilton-Jacobi equations of contact type. We also obtain a vanishing contact structure result for relevant Cauchy problems which can be…

We establish the local well-posedness of the general Ericksen-Leslie system in liquid crystals with the initial velocity and director field in $H^1 \times H_b^2$. In particular, we prove that the solutions of the Ginzburg-Landau…

We present a derivation of a coarse-grained model from the Langevin dynamics. The focus is placed on the memory kernel function and the fluctuation-dissipation theorem. Also presented is an hierarchy of approximations for the memory and…

We show a connection between global unconstrained optimization of a continuous function $f$ and weak KAM theory for an eikonal-type equation arising also in ergodic control. A solution $v$ of the critical Hamilton-Jacobi equation is built…