Hamilton Jacobi Equations Theory And Applications

Author : Hung V. Tran
Publisher : American Mathematical Soc.
Page : 322 pages
File Size : 48,5 Mb
Release : 2021-08-16
Category : Education
ISBN : 9781470465117

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Hamilton–Jacobi Equations: Theory and Applications by Hung V. Tran Pdf

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.

Author : Hung Vinh Tran
Publisher : American Mathematical Soc.
Page : 322 pages
File Size : 46,9 Mb
Release : 2021-09-17
Category : Education
ISBN : 9781470465551

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Hamilton-Jacobi Equations: Theory and Applications by Hung Vinh Tran Pdf

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.

Author : Yves Achdou,Guy Barles,Hitoshi Ishii,Grigory L. Litvinov
Publisher : Springer
Page : 301 pages
File Size : 40,7 Mb
Release : 2013-05-24
Category : Mathematics
ISBN : 9783642364334

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Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications by Yves Achdou,Guy Barles,Hitoshi Ishii,Grigory L. Litvinov Pdf

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 : Guy Barles,Emmanuel Chasseigne
Publisher : Springer Nature
Page : 569 pages
File Size : 48,6 Mb
Release : 2024-01-30
Category : Mathematics
ISBN : 9783031493713

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On Modern Approaches of Hamilton-Jacobi Equations and Control Problems with Discontinuities by Guy Barles,Emmanuel Chasseigne Pdf

This monograph presents the most recent developments in the study of Hamilton-Jacobi Equations and control problems with discontinuities, mainly from the viewpoint of partial differential equations. Two main cases are investigated in detail: the case of codimension 1 discontinuities and the stratified case in which the discontinuities can be of any codimensions. In both, connections with deterministic control problems are carefully studied, and numerous examples and applications are illustrated throughout the text. After an initial section that provides a “toolbox” containing key results which will be used throughout the text, Parts II and III completely describe several recently introduced approaches to treat problems involving either codimension 1 discontinuities or networks. The remaining sections are concerned with stratified problems either in the whole space R^N or in bounded or unbounded domains with state-constraints. In particular, the use of stratified solutions to treat problems with boundary conditions, where both the boundary may be non-smooth and the data may present discontinuities, is developed. Many applications to concrete problems are explored throughout the text – such as Kolmogorov-Petrovsky-Piskunov (KPP) type problems, large deviations, level-sets approach, large time behavior, and homogenization – and several key open problems are presented. This monograph will be of interest to graduate students and researchers working in deterministic control problems and Hamilton-Jacobi Equations, network problems, or scalar conservation laws.

Author : Piermarco Cannarsa,Carlo Sinestrari
Publisher : Springer Science & Business Media
Page : 304 pages
File Size : 41,8 Mb
Release : 2007-12-31
Category : Mathematics
ISBN : 9780817644130

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Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control by Piermarco Cannarsa,Carlo Sinestrari Pdf

* A comprehensive and systematic exposition of the properties of semiconcave functions and their various applications, particularly to optimal control problems, by leading experts in the field * A central role in the present work is reserved for the study of singularities * Graduate students and researchers in optimal control, the calculus of variations, and PDEs will find this book useful as a reference work on modern dynamic programming for nonlinear control systems

Author : Benton
Publisher : Academic Press
Page : 146 pages
File Size : 55,5 Mb
Release : 1977-06-29
Category : Computers
ISBN : 9780080956404

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Hamilton-Jacobi Equation: A Global Approach by Benton Pdf

Hamilton-Jacobi Equation: A Global Approach

Author : Hanno Rund
Publisher : Krieger Publishing Company
Page : 422 pages
File Size : 52,6 Mb
Release : 1966
Category : Mathematics
ISBN : UOM:39015026555543

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The Hamilton-Jacobi Theory in the Calculus of Variations by Hanno Rund Pdf

Author : Lopez Velazquez Gustavo
Publisher : World Scientific Publishing Company
Page : 200 pages
File Size : 55,5 Mb
Release : 2012-03-21
Category : Science
ISBN : 9789814397506

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Partial Differential Equations Of First Order And Their Applications To Physics (2nd Edition) by Lopez Velazquez Gustavo Pdf

This book tries to point out the mathematical importance of the Partial Differential Equations of First Order (PDEFO) in Physics and Applied Sciences. The intention is to provide mathematicians with a wide view of the applications of this branch in physics, and to give physicists and applied scientists a powerful tool for solving some problems appearing in Classical Mechanics, Quantum Mechanics, Optics, and General Relativity. This book is intended for senior or first year graduate students in mathematics, physics, or engineering curricula.This book is unique in the sense that it covers the applications of PDEFO in several branches of applied mathematics, and fills the theoretical gap between the formal mathematical presentation of the theory and the pure applied tool to physical problems that are contained in other books.Improvements made in this second edition include corrected typographical errors; rewritten text to improve the flow and enrich the material; added exercises in all chapters; new applications in Chapters 1, 2, and 5 and expanded examples.

Author : Mark D. Ardema
Publisher : Springer Science & Business Media
Page : 364 pages
File Size : 55,5 Mb
Release : 2005
Category : Science
ISBN : 0306486814

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Analytical Dynamics by Mark D. Ardema Pdf

This book takes a traditional approach to the development of the methods of analytical dynamics, using two types of examples throughout: simple illustrations of key results and thorough applications to complex, real-life problems.

Author : Gustavo López
Publisher : World Scientific Publishing Company
Page : 124 pages
File Size : 44,6 Mb
Release : 1999-12-16
Category : Mathematics
ISBN : 9789813105386

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Partial Differential Equations of First Order and Their Applications to Physics by Gustavo López Pdf

This book is about the theory and applications of Partial Differential Equations of First Order (PDEFO). Many interesting topics in physics such as constant motion of dynamical systems, renormalization theory, Lagrange transformation, ray trajectories, and Hamilton–Jacobi theory are or can be formulated in terms of partial differential equations of first order. In this book, the author illustrates the utility of the powerful method of PDEFO in physics, and also shows how PDEFO are useful for solving practical problems in different branches of science. The book focuses mainly on the applications of PDEFO, and the mathematical formalism is treated carefully but without diverging from the main objective of the book. Request Inspection Copy

Author : R. Miron
Publisher : Springer Science & Business Media
Page : 247 pages
File Size : 40,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401000703

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The Geometry of Higher-Order Hamilton Spaces by R. Miron Pdf

This book is the first to present an overview of higher-order Hamilton geometry with applications to higher-order Hamiltonian mechanics. It is a direct continuation of the book The Geometry of Hamilton and Lagrange Spaces, (Kluwer Academic Publishers, 2001). It contains the general theory of higher order Hamilton spaces H(k)n, k>=1, semisprays, the canonical nonlinear connection, the N-linear metrical connection and their structure equations, and the Riemannian almost contact metrical model of these spaces. In addition, the volume also describes new developments such as variational principles for higher order Hamiltonians; Hamilton-Jacobi equations; higher order energies and law of conservation; Noether symmetries; Hamilton subspaces of order k and their fundamental equations. The duality, via Legendre transformation, between Hamilton spaces of order k and Lagrange spaces of the same order is pointed out. Also, the geometry of Cartan spaces of order k =1 is investigated in detail. This theory is useful in the construction of geometrical models in theoretical physics, mechanics, dynamical systems, optimal control, biology, economy etc.

Author : Maurizio Falcone,Roberto Ferretti
Publisher : SIAM
Page : 331 pages
File Size : 50,5 Mb
Release : 2014-01-31
Category : Mathematics
ISBN : 9781611973044

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Semi-Lagrangian Approximation Schemes for Linear and Hamilton-Jacobi Equations by Maurizio Falcone,Roberto Ferretti Pdf

This largely self-contained book provides a unified framework of semi-Lagrangian strategy for the approximation of hyperbolic PDEs, with a special focus on Hamilton-Jacobi equations. The authors provide a rigorous discussion of the theory of viscosity solutions and the concepts underlying the construction and analysis of difference schemes; they then proceed to high-order semi-Lagrangian schemes and their applications to problems in fluid dynamics, front propagation, optimal control, and image processing. The developments covered in the text and the references come from a wide range of literature.

Author : Viorel Barbu,Giuseppe Da Prato
Publisher : Pitman Advanced Publishing Program
Page : 188 pages
File Size : 51,8 Mb
Release : 1983
Category : Hamilton-Jacobi equations
ISBN : UCAL:B4405593

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Hamilton-Jacobi Equations in Hilbert Spaces by Viorel Barbu,Giuseppe Da Prato Pdf

Author : Pierre-Louis Lions
Publisher : Pitman Publishing
Page : 332 pages
File Size : 47,5 Mb
Release : 1982
Category : Cauchy problem
ISBN : UCAL:B4405522

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Generalized Solutions of Hamilton-Jacobi Equations by Pierre-Louis Lions Pdf

Author : Hiroyoshi Mitake,Hung V. Tran,Nam Q. Le
Publisher : Springer
Page : 233 pages
File Size : 46,5 Mb
Release : 2017-06-14
Category : Mathematics
ISBN : 9783319542089

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Dynamical and Geometric Aspects of Hamilton-Jacobi and Linearized Monge-Ampère Equations by Hiroyoshi Mitake,Hung V. Tran,Nam Q. Le Pdf

Consisting of two parts, the first part of this volume is an essentially self-contained exposition of the geometric aspects of local and global regularity theory for the Monge–Ampère and linearized Monge–Ampère equations. As an application, we solve the second boundary value problem of the prescribed affine mean curvature equation, which can be viewed as a coupling of the latter two equations. Of interest in its own right, the linearized Monge–Ampère equation also has deep connections and applications in analysis, fluid mechanics and geometry, including the semi-geostrophic equations in atmospheric flows, the affine maximal surface equation in affine geometry and the problem of finding Kahler metrics of constant scalar curvature in complex geometry. Among other topics, the second part provides a thorough exposition of the large time behavior and discounted approximation of Hamilton–Jacobi equations, which have received much attention in the last two decades, and a new approach to the subject, the nonlinear adjoint method, is introduced. The appendix offers a short introduction to the theory of viscosity solutions of first-order Hamilton–Jacobi equations.