Existence and uniqueness of viscosity solution for Hamilton-Jacobi equation with discontinuous coefficients dependent on time

The main result is a proof of the existence of a unique viscosity solution for Hamilton-Jacobi equation, where the hamiltonian is discontinuous with respect to variable, usually interpreted as the spatial one. Obtained generalized solution is continuous, but not necessarily differentiable.

On the Hamilton-Jacobi equation in the framework of generalized functions

In this work we study, in the framework of Colombeau`s generalized functions, the Hamilton-Jacobi equation with a given initial condition. We have obtained theorems on existence of solutions and in some cases uniqueness. Our technique is adapted from the classical method of characteristics with a wide use of generalized functions. We were led also to obtain some general results on invertibility and also on ordinary differential equations of such generalized functions. (C) 2011 Elsevier Inc. All rights reserved.

Hamilton-Jacobi approach to Berezinian singular systems

In this work we present a formal generalization of the Hamilton-Jacobi formalism, recently developed For singular systems, to include the case of Lagrangians containing variables which are elements of Berezin algebra. We derive the Hamilton-Jacobi equation for such systems, analyzing the singular case in order to obtain the equations of motion as total differential equations and study the integrability conditions for such equations. An example is solved using both Hamilton-Jacobi and Dirac's Hamiltonian formalisms and the results are compared. (C) 1998 Academic Press.

Formalismo de Hamilton-Jacobi à la Carathéodory

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Formalismo de Hamilton-Jacobi à la Carathéodory. Parte 2: sistemas singulares

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Méthodes rapides et efficaces pour la résolution numérique d'équations de type Hamilton-Jacobi avec application à la simulation de feux de forêt

Cette thèse est divisée en trois chapitres. Le premier explique comment utiliser la méthode «level-set» de manière rigoureuse pour faire la simulation de feux de forêt en utilisant comme modèle physique pour la propagation le modèle de l'ellipse de Richards. Le second présente un nouveau schéma semi-implicite avec une preuve de convergence pour la solution d'une équation de type Hamilton-Jacobi anisotrope. L'avantage principal de cette méthode est qu'elle permet de réutiliser des solutions à des problèmes «proches» pour accélérer le calcul. Une autre application de ce schéma est l'homogénéisation. Le troisième chapitre montre comment utiliser les méthodes numériques des deux premiers chapitres pour étudier l'influence de variations à petites échelles dans la vitesse du vent sur la propagation d'un feu de forêt à l'aide de la théorie de l'homogénéisation.

Estudo clássico completo do formalismo de Hamilton-Jacobi

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Hamilton Jacobi theory for constrained systems

We extend the HamiltonJacobi formulation to constrained dynamical systems. The discussion covers both the case of first-class constraints alone and that of first- and second-class constraints combined. The HamiltonDirac equations are recovered as characteristic of the system of partial differential equations satisfied by the HamiltonJacobi function.

Hamilton-Jacobi theory for constrained systems

We extend the HamiltonJacobi formulation to constrained dynamical systems. The discussion covers both the case of first-class constraints alone and that of first- and second-class constraints combined. The HamiltonDirac equations are recovered as characteristic of the system of partial differential equations satisfied by the HamiltonJacobi function.

The Teleparallel Lagrangian and Hamilton-Jacobi formalism

We analyze the Teleparallel Equivalent of General Relativity (TEGR) from the point of view of Hamilton-Jacobi approach for singular systems.

The Hamilton-Jacobi approach to Teleparallelism

We intend to analyse the constraint structure of Teleparallelism employing the Hamilton-Jacobi formalism for singular systems. This study is conducted without using an ADM 3+1 decomposition and without fixing time gauge condition. It can be verified that the field equations constitute an integrable system.

Generalization of the Hamilton-Jacobi approach for higher-order singular systems

We generalize the Hamilton-Jacobi formulation for higher-order singular systems and obtain the equations of motion as total differential equations. To do this we first study the constraints structure present in such systems.

Hamilton-Jacobi formalism for linearized gravity

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Non-involutive constrained systems and Hamilton-Jacobi formalism

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Hamilton-Jacobi approach for first order actions and theories with higher derivatives

In this work, we analyze systems described by Lagrangians with higher order derivatives in the context of the Hamilton-Jacobi formalism for first order actions. Two different approaches are studied here: the first one is analogous to the description of theories with higher derivatives in the hamiltonian formalism according to [D.M. Gitman, S.L. Lyakhovich, I.V. Tyutin, Soviet Phys. J. 26 (1983) 730; D.M. Gitman, I.V. Tyutin, Quantization of Fields with Constraints, Springer-Verlag, New York, Berlin, 1990] the second treats the case where degenerate coordinate are present, in an analogy to reference [D.M. Gitman, I.V. Tyutin, Nucl. Phys. B 630 (2002) 509]. Several examples are analyzed where a comparison between both approaches is made. (C) 2007 Elsevier B.V. All rights reserved.