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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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Quantum Hamilton-Jacobi Equation [PDF]
Physical Review Letters, 1998 The nontrivial transformation of the phase space path integral measure under certain discretized analogues of canonical transformations is computed. This Jacobian is used to derive a quantum analogue of the Hamilton-Jacobi equation for the generating function of a canonical transformation that maps any quantum system to a system with a vanishing ...
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Singularities of Solutions of Hamilton–Jacobi Equations [PDF]
Milan Journal of Mathematics, 2021 AbstractThis is a survey paper on the quantitative analysis of the propagation of singularities for the viscosity solutions to Hamilton–Jacobi equations in the past decades. We also review further applications of the theory to various fields such as Riemannian geometry, Hamiltonian dynamical systems and partial differential equations.
Piermarco Cannarsa, Wei Cheng
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Advances in High Energy Physics, 2016 Based on semiclassical tunneling method, we focus on charged fermions tunneling from higher-dimensional Reissner-Nordström black hole. We first simplify the Dirac equation by semiclassical approximation, and then a semiclassical Hamilton-Jacobi equation ...
ShuZheng Yang, Dan Wen, Kai Lin
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Hamilton-Jacobi Method for Mechanical Systems on Time Scales
Complexity, 2018 This paper presents the Hamilton-Jacobi method for integrating the equations of motion of mechanical systems on time scales. We give the criterion and four basic forms of canonical transformation on time scales.
Xiang-Hua Zhai, Yi Zhang
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SICE Journal of Control, Measurement, and System Integration, 2020 This paper presents a numerical approach to solve the Hamilton-Jacobi-Bellman (HJB) equation, which arises in nonlinear optimal control. In this approach, we first use the successive approximation to reduce the HJB equation, a nonlinear partial ...
Ichiro Maruta +2 more
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Optimal control of the propagation of a graph in inhomogeneous media [PDF]
, 2009 We study an optimal control problem for viscosity solutions of a Hamilton–Jacobi equation describing the propagation of a one-dimensional graph with the control being the speed function.
Deckelnick, Klaus +5 more
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Frontiers in Physics, 2023 In this work, we present two finite-dimensional Lie–Poisson Hamiltonian systems associated with the Hirota–Satsuma modified Boussinesq equation by using the nonlinearization method. Moreover, the separation of variables on the common level set of Casimir
Xue Geng, Dianlou Du, Xianguo Geng
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Hamilton-Jacobi Equations on Graph and Applications [PDF]
Potential Analysis, 2017 This paper introduces a notion of gradient and an infimal-convolution operator that extend properties of solutions of Hamilton Jacobi equations to more general spaces, in particular to graphs. As a main application, the hypercontractivity of this class of infimal-convolution operators is connected to some discrete version of the log-Sobolev inequality ...
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Optimal Consumption in a Stochastic Ramsey Model with Cobb-Douglas Production Function
International Journal of Mathematics and Mathematical Sciences, 2013 A stochastic Ramsey model is studied with the Cobb-Douglas production function maximizing the expected discounted utility of consumption. We transformed the Hamilton-Jacobi-Bellman (HJB) equation associated with the stochastic Ramsey model so as to ...
Md. Azizul Baten, Anton Abdulbasah Kamil
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