Junction Conditions for Hamilton–Jacobi Equations for Solving Real-Time Traffic Flow Problems
IEEE Access, 2019 In this paper, we propose junction conditions for discontinuities due to local perturbation, diverging, merging, and multi-in-multi-out junctions. Traffic flows on junctions can be described by a system of coupled Hamilton-Jacobi equations.
Linfeng Zhang +3 more
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Hamilton-Jacobi Theory for Degenerate Lagrangian Systems with Holonomic and Nonholonomic Constraints [PDF]
, 2012 We extend Hamilton-Jacobi theory to Lagrange-Dirac (or implicit Lagrangian) systems, a generalized formulation of Lagrangian mechanics that can incorporate degenerate Lagrangians as well as holonomic and nonholonomic constraints.
Abraham R. +18 more
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Hypercontractivity of Hamilton–Jacobi equations
Journal de Mathématiques Pures et Appliquées, 2001 Using the equivalence of logarithmic Sobolev inequalities and hypercontractivity of the associated heat semigroup proved by \textit{L. Gross} [Am. J. Math. 97(1975), 1061--1083 (1976; Zbl 0318.46049)], the authors show that logarithmic Sobolev inequalities are similarly related to hypercontractivity of the solutions of Hamilton-Jacobi equations.
Bobkov, Sergey G +2 more
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Bounded-From-Below Solutions of the Hamilton-Jacobi Equation for Optimal Control Problems with Exit Times: Vanishing Lagrangians, Eikonal Equations, and Shape-From-Shading [PDF]
, 2003 We study the Hamilton-Jacobi equation for undiscounted exit time control problems with general nonnegative Lagrangians using the dynamic programming approach.
Malisoff, Michael
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Hamilton Jacobi Equations with Obstacles [PDF]
Archive for Rational Mechanics and Analysis, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
De Lellis, Camillo, Robyr, R
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Almost Periodic Viscosity Solutions of Nonlinear Parabolic Equations
Boundary Value Problems, 2009 We generalize the comparison result 2007 on Hamilton-Jacobi equations to nonlinear parabolic equations, then by using Perron's method to study the existence and uniqueness of time almost periodic viscosity solutions of nonlinear parabolic equations ...
Shilin Zhang, Daxiong Piao
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Unified formalism for the generalized kth-order Hamilton-Jacobi problem [PDF]
, 2013 The geometric formulation of the Hamilton-Jacobi theory enables us to generalize it to systems of higher-order ordinary differential equations. In this work we introduce the unified Lagrangian-Hamiltonian formalism for the geometric Hamilton-Jacobi ...
Colombo, Leonardo +3 more
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Numerical discretization of Hamilton--Jacobi equations on networks
Networks and Heterogeneous Media, 2013 We discuss a numerical discretization of Hamilton--Jacobi equations on networks. The latter arise for example as reformulationof the Lighthill--Whitham--Richards traffic flow model.
Simone Göttlich +2 more
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Some non monotone schemes for Hamilton-Jacobi-Bellman equations [PDF]
ESAIM: Proceedings and Surveys, 2019 We extend the theory of Barles Jakobsen [3] for a class of almost monotone schemes to solve stationary Hamilton Jacobi Bellman equations. We show that the monotonicity of the schemes can be relaxed still leading to the convergence to the viscosity ...
Warin Xavier
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Estimates for multiple stochastic integrals and stochastic Hamilton-Jacobi equations [PDF]
, 2004 We study stochastic Hamilton-Jacobi-Bellman equations and the corresponding Hamiltonian systems driven by jump-type Lévy processes. The main objective of the present paper is to show existence, uniqueness and a (locally in time) diffeomorphism ...
Kolokoltsov, V. N. (Vasiliĭ Nikitich) +2 more
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