Results 1 to 10 of about 1,473,150 (249)
Hamilton–Jacobi equations [PDF]
, 2010 In this chapter we discuss numerical methods for the solution of general Hamilton-Jacobi equations of the form $${\phi _t} + H\left( {\nabla \phi } \right) = 0$$ (5.1) where H can be a function of both space and time. In three spatial dimensions, we can write $${\phi _t} + H\left( {{\phi _x},{\phi _y},{\phi _z}} \right) = 0$$ (5.2 ...
Stanley Osher, Ronald Fedkiw
+5 more sources
Hamilton Jacobi Equations with Obstacles [PDF]
Archive for Rational Mechanics and Analysis, 2010 We consider a problem in the theory of optimal control proposed for the first time by Bressan. We characterize the associated minimum time function using tools from geometric measure theory and we obtain, as a corollary, an existence theorem for a related variational problem.
De Lellis, Camillo, Robyr, R
openaire +1 more source
Existence of solutions to contact mean-field games of first order
Advanced Nonlinear Studies, 2022 This paper deals with the existence of solutions of a class of contact mean-field game systems of first order consisting of a contact Hamilton-Jacobi equation and a continuity equation.
Hu Xiaotian, Wang Kaizhi
doaj +1 more source
Symmetries of the Hamilton–Jacobi equation [PDF]
Journal of Mathematical Physics, 1977 We present a detailed discussion of the infinit esimal symmetries of the Hamilton-Jacobi equation (an arbitrary first order partial equation) Our presentation clucidates the role played by the characteristic system in determining the symmetries. We then specialize to the case of a free particle in one space and one time dimension, and study of local ...
Boyer, C.P., Kalnins, Ernie G.
openaire +3 more sources
Resurgence in a Hamilton-Jacobi equation [PDF]
Annales de l'Institut Fourier, 2003 We study the resurgent structure associated with a Hamilton-Jacobi equation. This equation is obtained as the inner equation when studying the separatrix splitting problem for a perturbed pendulum via complex matching. We derive the Bridge equation, which encompasses infinitely many resurgent relations satisfied by the formal solution ...
Olivé, Carme +2 more
openaire +2 more sources
The Quantum Hamilton–Jacobi Equation and the Link Between Classical and Quantum Mechanics
Quanta, 2022 We study how the classical Hamilton's principal and characteristic functions are generated from the solutions of the quantum Hamilton–Jacobi equation.
Mario Fusco Girard
doaj +1 more source
On controlled Hamilton and Hamilton–Jacobi differential equations of higher-order
Scientific Reports, 2022 In this paper, we investigate the nonlinear dynamics associated with controlled Lagrangians involving higher-order derivatives. More precisely, we establish the controlled higher-order Hamilton ordinary differential equations (ODEs) and Hamilton–Jacobi ...
Savin Treanţă +2 more
doaj +1 more source
Hamilton–Jacobi equations on an evolving surface [PDF]
Mathematics of Computation, 2019 We consider the well-posedness and numerical approximation of a Hamilton--Jacobi equation on an evolving hypersurface in $\mathbb R^3$. Definitions of viscosity sub- and supersolutions are extended in a natural way to evolving hypersurfaces and provide uniqueness by comparison. An explicit in time monotone numerical approximation is derived on evolving
Klaus Deckelnick +3 more
openaire +3 more sources
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
CAPUZZO DOLCETTA, Italo, P. L. Lions
openaire +1 more source
THE HAMILTON–JACOBI EQUATION ON LIE AFFGEBROIDS [PDF]
International Journal of Geometric Methods in Modern Physics, 2006 The Hamilton–Jacobi equation for a Hamiltonian section on a Lie affgebroid is introduced and some examples are discussed.
Marrero, J. C., Sosa, D.
openaire +3 more sources