相关论文: The Vanishing Discount problem for Hamilton-Jacobi…

In the paper [P. Cannarsa, C. Mendico, Asymptotic analysis for Hamilton-Jacobi- Bellman equations on Euclidean space, (2021) Arxiv], we proved the existence of the limit as the time horizon goes to infinity of the averaged value function of…

In this paper, we investigate the compactness of nonnegative solutions to a critical sub-elliptic equation with a nonnegative potential on the Heisenberg group. We establish that the solution set is compact provided the potential satisfies…

We study the large-time behavior of bounded from below solutions of parabolic viscous Hamilton-Jacobi Equations in the whole space $\mathbb{R}^N$ in the case of superquadratic Hamiltonians. Existence and uniqueness of such solutions are…

This article establishes a stochastic homogenization result for the first order Hamilton-Jacobi equation on a Riemannian manifold $M$, in the context of a stationary ergodic random environment. The setting involves a finitely generated…

We extend to higher dimensions the notion of Birkhoff attractor of a dissipative map. We prove that this notion coincides with the classical Birkhoff attractor. We prove that for the dissipative system associated to the discounted…

We consider a certain ultrahyperbolic equation in a Euclidean space being a generalization of Klein-Gordon-Fock equation. The behavior of solutions at points tending to infinity along timelike directions is studied. We examine the issue of…

The optimal \(H_{\infty}\) control problem over an infinite time horizon, which incorporates a performance function with a discount factor \(e^{-\alpha t}\) (\(\alpha > 0\)), is important in various fields. Solving this optimal…

We consider the total energy decay together with L^2-bound of the solution itself of the Cauchy problem for wave equations with a localized damping and a short-range potential. We treat it in the one dimensional Euclidean space R. We adopt…

We prove exponential convergence to time-periodic states of the solutions of time-periodic Hamilton-Jacobi equations on the torus, assuming that the Aubry set is the union of a finite number of hyperbolic periodic orbits of the the Euler…

The aim of this work is to deal with a discontinuous Hamilton-Jacobi equation in the whole euclidian N-dimensional space, associated to a possibly unbounded optimal control problem. Here, the discontinuities are located on a hyperplane and…

We use a Lagrangian regularity perspective to discuss resolvent estimates near zero energy on Riemannian scattering, i.e. asymptotically conic, spaces, and their generalizations. In addition to the Lagrangian perspective we introduce and…

Nonholonomic mechanical systems have been attracting more interest in recent years because of their rich geometric properties and their applications in Engineering. In all generality, we discuss the reduction of a Hamilton-Jacobi theory for…

We study a selection problem for degenerate viscous Hamilton--Jacobi equations with convex Hamiltonians, in which the approximation procedure combines a nonlinear discounted approximation with a small potential perturbation. A key question…

We provide some new integral estimates for solutions to Hamilton-Jacobi equations and we discuss several consequences, ranging from $L^p$-rates of convergence for the vanishing viscosity approximation to regularizing effects for the Cauchy…

We develop two approximation schemes for solving the cell equation and the discounted cell equation using Aubry-Mather-Fathi theory. The Hamiltonian is supposed to be Tonelli, time-independent , and periodic in space. By Legendre transform…

We develop a constructive procedure for arriving at the Hamilton-Jacobi framework for the so-called affine in acceleration theories by analysing the canonical constraint structure. We find two scenarios in dependence of the order of the…

We discuss the application of the method of the gaugeless Hamiltonian reduction to general relativity. This method is based on explicit resolving the global part of the energy constraint and on identification of one of the metric components…

In 2002, Fatiha Alabau, Piermarco Cannarsa and Vilmos Komornik investigated the extent of asymptotic stability of the null solution for weakly coupled partially damped equations of the second order in time. The main point is that the…

We consider a continuous coercive Hamiltonian $H$ on the cotangent bundle of the compact connected manifold $M$ which is convex in the momentum. If $u_\lambda:M\to\mathbb R$ is the viscosity solution of the discounted equation $$ \lambda…

A new formulation of the Hamiltonian dynamics of the gravitational field interacting with(non-dissipative) thermo-elastic matter is discussed. It is based on a gauge condition which allows us to encode the six degrees of freedom of the…