Related papers: Hamilton-Jacobi-Bellman equations on graphs
We consider a scheme of Semi-Lagrangian (SL) type for the numerical solution of Hamilton-Jacobi (HJ) equation on unstructured triangular grids. As it is well known, SL schemes are not well suited for unstructured grids, due to the cost of…
We consider the homogenization of Hamilton-Jacobi equations and degenerate Bellman equations in stationary, ergodic, unbounded environments. We prove that, as the microscopic scale tends to zero, the equation averages to a deterministic…
This article is a continuation of a previous work where we studied infinite horizon control problems for which the dynamic, running cost and control space may be different in two half-spaces of some euclidian space $\R^N$. In this article…
This paper presents a new methodology to craft navigation functions for nonlinear systems with stochastic uncertainty. The method relies on the transformation of the Hamilton-Jacobi-Bellman (HJB) equation into a linear partial differential…
We study the solution theory of the whole-space static (elliptic) Hamilton-Jacobi-Bellman (HJB) equation in spectral Barron spaces. We prove that under the assumption that the coefficients involved are spectral Barron functions and the…
We consider the problem of time-optimal path planning for simple nonholonomic vehicles. In previous similar work, the vehicle has been simplified to a point mass and the obstacles have been stationary. Our formulation accounts for a…
This survey paper is focused on qualitative and numerical analyses of fully nonlinear partial differential equations of parabolic type arising in financial mathematics. The main purpose is to review various non-linear extensions of the…
We prove first-order convergence of semi-discrete monotone finite difference schemes for Hamilton--Jacobi equations on the Wasserstein space over a finite graph. A central challenge is the boundary degeneracy of the Wasserstein simplex,…
This paper is concerned with a comparison principle for viscosity solutions to Hamilton-Jacobi (HJ), -Bellman (HJB), and -Isaacs (HJI) equations for general classes of partial integro-differential operators. Our approach innovates in three…
We investigate a singular perturbation for Hamilton-Jacobi equations in an open subset of two dimensional Euclidean space, where the set is determined through a Hamiltonian function and the Hamilton-Jacobi equations are the dynamic…
In this paper, we assume that $q>0$, $p>1$ and $s\in(0,1)$ , and consider the following nonlinear fractional p-Laplacian equations on finite graphs: \begin{equation*} \left\{ \begin{array}{lll} \partial_t u^q(x,t)+(-\Delta)_p^su=0,\\[15pt]…
The rarely used Hamilton-Jacobi equation has been utilized as an elegant way to find the trajectories of mechanical systems and to derive symplectic maps. Further, the exact solution in kick approximation of Hamilton's equations of motion…
This work proposes and studies numerical schemes for initial value problems of Hamilton--Jacobi equations (HJEs) with a graph individual noise on the Wasserstein space on graphs. Numerically solving such equations is particularly…
In this note we study the convergence of monotone P1 finite element methods on unstructured meshes for fully non-linear Hamilton-Jacobi-Bellman equations arising from stochastic optimal control problems with possibly degenerate, isotropic…
Highly concentrated patterns have been observed in a spatially heterogeneous, nonlocal, model of BGK type implementing a velocity-jump process. We study both a linear and a nonlinear case and describe the concentration profile. In…
We extend some aspects of the Hamilton-Jacobi theory to the category of stochastic Hamiltonian dynamical systems. More specifically, we show that the stochastic action satisfies the Hamilton-Jacobi equation when, as in the classical…
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 order to describe the impact of different geometric structures and constraints for the dynamics of a regular controlled Hamiltonian system, in this paper, we first define a kind of controlled magnetic Hamiltonian (CMH) system, and give a…
We study a class of Hamilton-Jacobi partial differential equations in the space of probability measures. In the first part of this paper, we prove comparison principles (implying uniqueness) for this class. In the second part, we establish…
In this paper, we construct Hamilton-Jacobi equations for a great variety of mechanical systems (nonholonomic systems subjected to linear or affine constraints, dissipative systems subjected to external forces, time-dependent mechanical…