On subsolutions and supersolutions of discrete Hamilton-Jacobi-Bellman equation PDF Download

Author: R. L. V. Gonzales
Publisher:
ISBN:
Category :
Languages : fr
Pages : 15

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Author: Roberto L. V. Gonzalez
Publisher:
ISBN:
Category : Hamilton-Jacobi equations
Languages : en
Pages : 15

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Book Description

Author: Roberto L. V. Gonzalez
Publisher:
ISBN:
Category :
Languages : en
Pages : 14

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Book Description

Author: Yves Achdou
Publisher: Springer
ISBN: 3642364330
Category : Mathematics
Languages : en
Pages : 316

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Book Description
These Lecture Notes contain the material relative to the courses given at the CIME summer school held in Cetraro, Italy from August 29 to September 3, 2011. The topic was "Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications". The courses dealt mostly with the following subjects: first order and second order Hamilton-Jacobi-Bellman equations, properties of viscosity solutions, asymptotic behaviors, mean field games, approximation and numerical methods, idempotent analysis. The content of the courses ranged from an introduction to viscosity solutions to quite advanced topics, at the cutting edge of research in the field. We believe that they opened perspectives on new and delicate issues. These lecture notes contain four contributions by Yves Achdou (Finite Difference Methods for Mean Field Games), Guy Barles (An Introduction to the Theory of Viscosity Solutions for First-order Hamilton-Jacobi Equations and Applications), Hitoshi Ishii (A Short Introduction to Viscosity Solutions and the Large Time Behavior of Solutions of Hamilton-Jacobi Equations) and Grigory Litvinov (Idempotent/Tropical Analysis, the Hamilton-Jacobi and Bellman Equations).

Author: Pierre-Louis Lions
Publisher: Pitman Publishing
ISBN:
Category : Mathematics
Languages : en
Pages : 332

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Book Description
This volume contains a complete and self-contained treatment of Hamilton-Jacobi equations. The author gives a new presentation of classical methods and of the relations between Hamilton-Jacobi equations and other fields. This complete treatment of both classical and recent aspects of the subject is presented in such a way that it requires only elementary notions of analysis and partial differential equations.

Author:
Publisher:
ISBN:
Category : Statistics
Languages : en
Pages : 1092

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Author: Naoki Yamada
Publisher:
ISBN:
Category :
Languages : en
Pages : 24

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As the first order Hamilton Jacobi equation is related to a control problem associated with ordinary differential equations, the Hamilton Jacobi Bellman (HJB) equation arises from a control problem with random noise. In the stationary problem, the HJB equation has the form sup when alpha is an element of A of (L superscript alpha)u - (f superscript and alpha = 0 where L superscript alpha are second order linear elliptic operators with parameter alpha an element of A. In this paper, we are concerned with the HJB equation of the form max

Author:
Publisher:
ISBN:
Category : Differentiable dynamical systems
Languages : en
Pages : 632

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Author: National Aeronautics and Space Administration (NASA)
Publisher: Createspace Independent Publishing Platform
ISBN: 9781720572312
Category :
Languages : en
Pages : 34

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We present the first fifth order, semi-discrete central upwind method for approximating solutions of multi-dimensional Hamilton-Jacobi equations. Unlike most of the commonly used high order upwind schemes, our scheme is formulated as a Godunov-type scheme. The scheme is based on the fluxes of Kurganov-Tadmor and Kurganov-Tadmor-Petrova, and is derived for an arbitrary number of space dimensions. A theorem establishing the monotonicity of these fluxes is provided. The spacial discretization is based on a weighted essentially non-oscillatory reconstruction of the derivative. The accuracy and stability properties of our scheme are demonstrated in a variety of examples. A comparison between our method and other fifth-order schemes for Hamilton-Jacobi equations shows that our method exhibits smaller errors without any increase in the complexity of the computations.Bryson, Steve and Levy, Doron and Biegel, Bryan (Technical Monitor)Ames Research CenterHAMILTON-JACOBI EQUATION; UPWIND SCHEMES (MATHEMATICS); DISCRETIZATION (MATHEMATICS); ACCURACY; DERIVATION; ERRORS; THEOREMS; MONOTONE FUNCTIONS; ESSENTIALLY NON-OSCILLATORY SCHEMES

Author: Hung V. Tran
Publisher: American Mathematical Soc.
ISBN: 1470465116
Category : Education
Languages : en
Pages : 322

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Book Description
This book gives an extensive survey of many important topics in the theory of Hamilton–Jacobi equations with particular emphasis on modern approaches and viewpoints. Firstly, the basic well-posedness theory of viscosity solutions for first-order Hamilton–Jacobi equations is covered. Then, the homogenization theory, a very active research topic since the late 1980s but not covered in any standard textbook, is discussed in depth. Afterwards, dynamical properties of solutions, the Aubry–Mather theory, and weak Kolmogorov–Arnold–Moser (KAM) theory are studied. Both dynamical and PDE approaches are introduced to investigate these theories. Connections between homogenization, dynamical aspects, and the optimal rate of convergence in homogenization theory are given as well. The book is self-contained and is useful for a course or for references. It can also serve as a gentle introductory reference to the homogenization theory.