相关论文: Aubry sets for weakly coupled systems of Hamilton-…

We study a class of weakly coupled systems of Hamilton{Jacobi equations at the critical level. We associate to it a family of scalar discounted equation. Using control{theoretic tech- niques we construct an algorithm which allows obtaining…

We establish the existence of smooth critical sub-solutions of the Hamilton-Jacobi equation on compact manifolds for smooth convex Hamiltonians, that is in the context of weak KAM theory, under the assumption that the Aubry set is the union…

We study a class of weakly coupled systems of Hamilton-acobi equations using the random frame introduced in a previous paper of Mitake-Siconolfi-Tran-Yamada. We provide a cycle condition characterizing the points of Aubry set. This…

We establish the stability under the formations of infimum and of convex combinations of subsolutions of convex Hamilton-Jacobi equations, some comparison and existence results for convex and coercive Hamilton-Jacobi equations with the…

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…

We extend the study of eikonal Hamilton-Jacobi equations posed on networks performed by Siconolfi and Sorrentino (Anal. PDE, 2018) to a more general setting. Their approach essentially exploits that such equations correspond to discrete…

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…

We prove that any continuous and convex stationary ergodic Hamiltonian admits critical subsolutions, which are strict outside the random Aubry set. They make up, in addition, a dense subset of all critical subsolutions with respect to a…

This paper is concerned with the study of Aubry-Mather and weak KAM theories for contact Hamiltonian systems with Hamiltonians $H(x,u,p)$ defined on $T^*M\times\mathbb{R}$, satisfying Tonelli conditions with respect to $p$ and…

In this paper we consider the notion of commutation for a pair of continuous and convex Hamiltonians, given in terms of commutation of their Lax- Oleinik semigroups. This is equivalent to the solvability of an associated multi- time…

We perform a qualitative analysis of the critical equation associated with a stationary ergodic Hamiltonian through a stochastic version of the metric method, where the notion of closed random stationary set, issued from stochastic…

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…

By exploiting the contact Hamiltonian dynamics $(T^*M\times\mathbb R,\Phi_t)$ around the Aubry set of contact Hamiltonian systems, we provide a relation among the Mather set, the $\Phi_t$-recurrent set, the strongly static set, the Aubry…

We study a class of weakly coupled Hamilton-Jacobi systems with a specific aim to perform a qualitative analysis in the spirit of weak KAM theory. Our main achievement is the definition of a family of related action functionals containing…

We consider Hamiltonians associated to optimal control problems for affine systems on the torus. They are not coercive and are possibly unbounded from below in the direction of the drift of the system. The main assumption is the strong…

We study the homogenization of first-order Hamilton-Jacobi equations on an infinite-dimensional Hilbert space, motivated by systems of infinitely many indistinguishable particles on the torus. A central difficulty is that the analysis takes…

Systems of Hamilton-Jacobi equations arise naturally when we study the optimal control problems with pathwise deterministic trajectories with random switching. In this work, we are interested in the large time behavior of weakly coupled…

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…

We study a strongly coupled system consisting of a parabolic equation and a singular Hamilton-Jacobi equation in one space dimension. This system describes the dynamics of dislocation densities in a material submitted to an exterior applied…

We consider homogenization for weakly coupled systems of Hamilton--Jacobi equations with fast switching rates. The fast switching rate terms force the solutions converge to the same limit, which is a solution of the effective equation. We…