相关论文: Convergence to time-periodic solutions in Hamilton…
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 study the optimal convergence rate for homogenization problem of convex Hamilton-Jacobi equations when the Hamitonian is periodic with respect to spatial and time variables, and notably time-dependent. We prove a result similar to that…
The objective of this paper is to find some inequalities satisfied by periodical solutions of multi-time Hamilton systems, when the Hamiltonian is convex. To our knowledge, this subject of first-order field theory is still open. Section 1…
In this paper we provide a rate of convergence for periodic homogenization of Hamilton-Jacobi-Bellman equations with nonlocal diffusion. The result is based on the regularity of the associated effective problem, where the convexity plays a…
We consider a Hamilton-Jacobi equation where the Hamiltonian is periodic in space and coercive and convex in momentum. Combining the representation formula from optimal control theory and a theorem of Alexander, originally proved in the…
We describe the asymptotic behaviour of solutions of unviscid Burgers equation on the circle with time-periodic forcing. These solutions converge to periodic states, but the period of these limit states may be greater than the period of the…
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 study the rate of convergence in periodic homogenization for convex Hamilton--Jacobi equations with multiscales, where the Hamiltonian $H=H(x, y, p): \mathbb{R}^n \times \mathbb{T}^n \times \mathbb{R}^n \to \mathbb{R }$ depends on both…
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…
In this paper we study homogenization for a class of monotone systems of first-order time-dependent periodic Hamilton-Jacobi equations. We characterize the Hamiltonians of the limit problem by appropriate cell problems. Hence we show the…
We prove that a Hamilton-Jacobi equation in 1D with periodic forcing has a set of generalized solutions such that each solution is a sum of linear and continuous periodic functions; we also give a condition of uniqueness of this solution in…
We prove the existence of $C^{1}$ critical subsolutions of the Hamilton-Jacobi equation for a time-periodic Hamiltonian system. We draw a consequence for the Minimal Action functional of the system.
We consider a numerical scheme for the one dimensional time dependent Hamilton-Jacobi equation in the periodic setting. We present a new and simple proof of the rate of convergence of the approximations based on the adjoint method recently…
In this paper, we study evolutive Hamilton Jacobi equations with Hamiltonians that are discontinuous in time, posed on a simple network consisting of two edges on the real line connected at a single junction. We introduce a notion of…
In this paper, we apply the geometric Hamilton--Jacobi theory to obtain solutions of Hamiltonian systems in Classical Mechanics, that are either compatible with a cosymplectic or a contact structure. As it is well known, the first structure…
In this paper, some of formulations of Hamilton-Jacobi equations for Hamiltonian system on Lie algebroids are given. Here we use the general properties of Lie algebroids to express and prove two geometric version of the Hamilton-Jacobi…
In this note, we discuss a class of time-dependent Hamilton-Jacobi equations depending on a function of time, this function being chosen in order to keep the maximum of the solution to the constant value 0. The main result of the note is…
In recent years it has been shown for hard sphere gas that, by retaining the correlation information, dynamical fluctuation and large deviation of empirical measure around Boltzmann equation could be proved, in addition to the classical…
This paper is devoted to the study of periodic solutions of Hamiltonian system $\dot z(t)=J \nabla H(z(t))$, where $H$ is symmetric under an action of a compact Lie group. We are looking for periodic solutions in a nearby of non-isolated…
Here, we study quantitative homogenization of first-order convex Hamilton-Jacobi equations with $(u/\varepsilon)$-periodic Hamiltonians which typically appear in dislocation dynamics. Firstly, we establish the optimal convergence rate by…