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Hamilton–Jacobi Equations [PDF]
, 2018 Hamilton–Jacobi equations are treated in the fifth chapter. Hamilton–Jacobi equations, their solutions, and the case of a time independent Hamiltonian are first recalled. Thirteen exercises are then solved, namely on a third harmonic oscillator, on a free falling particle, on a projectile ballistic flight, on a particle sliding on an inclined plane, on
Stanley Osher, Ronald Fedkiw
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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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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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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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GENERALIZED FRACTIONAL HYBRID HAMILTON–PONTRYAGIN EQUATIONS [PDF]
International Journal of Geometric Methods in Modern Physics, 2011 In this paper we present a new approach on the study of dynamical systems. Combining the two ways of expressing the uncertainty, using probabilistic theory and credibility theory, we have investigated the generalized fractional hybrid equations. We have introduced the concepts of generalized fractional Wiener process, generalized fractional Liu ...
Chis, O., Opris, Dumitru
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Hamilton-Jacobi Equations with State Constraints [PDF]
Transactions of the American Mathematical Society, 1990 In the present paper we consider Hamilton-Jacobi equations of the form H ( x , u , ∇ u ) = 0 , x ∈ Ω H(x,u,\nabla u) = 0,\;x \in \Omega , where Ω \Omega is a bounded open subset of
CAPUZZO DOLCETTA, Italo, P. L. Lions
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Hamilton–Jacobi equations for nonholonomic dynamics [PDF]
Journal of Mathematical Physics, 2005 We derive generalized Hamilton–Jacobi equations for dynamical systems subject to linear velocity constraints. As long as a solution of the generalized Hamilton–Jacobi equation exists, the action is actually minimized (not just extremized).
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Matemática Contemporânea, 1997 Summary: A special class of first order differential equations not solved for the derivative, implicit Hamilton equations, is defined as a Lagrangian submanifold of the tangent space of a symplectic manifold, and their typical phase portraits around singularities are studied.
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