Hamilton Jacobi Equations Approximations Numerical Analysis And Applications

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Hamilton Jacobi Equations Approximations Numerical Analysis And Applications
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Author : Yves Achdou
language : en
Publisher: Springer
Release Date : 2013-05-24
Hamilton Jacobi Equations Approximations Numerical Analysis And Applications written by Yves Achdou and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-24 with Mathematics categories.
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).
Hamilton Jacobi Bellman Equations
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Author : Dante Kalise
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-08-06
Hamilton Jacobi Bellman Equations written by Dante Kalise and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-06 with Mathematics categories.
Optimal feedback control arises in different areas such as aerospace engineering, chemical processing, resource economics, etc. In this context, the application of dynamic programming techniques leads to the solution of fully nonlinear Hamilton-Jacobi-Bellman equations. This book presents the state of the art in the numerical approximation of Hamilton-Jacobi-Bellman equations, including post-processing of Galerkin methods, high-order methods, boundary treatment in semi-Lagrangian schemes, reduced basis methods, comparison principles for viscosity solutions, max-plus methods, and the numerical approximation of Monge-Ampère equations. This book also features applications in the simulation of adaptive controllers and the control of nonlinear delay differential equations. Contents From a monotone probabilistic scheme to a probabilistic max-plus algorithm for solving Hamilton–Jacobi–Bellman equations Improving policies for Hamilton–Jacobi–Bellman equations by postprocessing Viability approach to simulation of an adaptive controller Galerkin approximations for the optimal control of nonlinear delay differential equations Efficient higher order time discretization schemes for Hamilton–Jacobi–Bellman equations based on diagonally implicit symplectic Runge–Kutta methods Numerical solution of the simple Monge–Ampere equation with nonconvex Dirichlet data on nonconvex domains On the notion of boundary conditions in comparison principles for viscosity solutions Boundary mesh refinement for semi-Lagrangian schemes A reduced basis method for the Hamilton–Jacobi–Bellman equation within the European Union Emission Trading Scheme
Hamilton Jacobi Equations Theory And Applications
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Author : Hung V. Tran
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-08-16
Hamilton Jacobi Equations Theory And Applications written by Hung V. Tran and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-16 with Education categories.
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.
Semi Lagrangian Approximation Schemes For Linear And Hamilton Jacobi Equations
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Author : Maurizio Falcone
language : en
Publisher: SIAM
Release Date : 2013-01-01
Semi Lagrangian Approximation Schemes For Linear And Hamilton Jacobi Equations written by Maurizio Falcone and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-01 with Mathematics categories.
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.
Numerical Methods For Viscosity Solutions And Applications
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Author : Maurizio Falcone
language : en
Publisher: World Scientific
Release Date : 2001
Numerical Methods For Viscosity Solutions And Applications written by Maurizio Falcone and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
The volume contains twelve papers dealing with the approximation of first and second order problems which arise in many fields of application including optimal control, image processing, geometrical optics and front propagation. Some contributions deal with new algorithms and technical issues related to their implementation. Other contributions are more theoretical, dealing with the convergence of approximation schemes. Many test problems have been examined to evaluate the performances of the algorithms. The volume can attract readers involved in the numerical approximation of differential models in the above-mentioned fields of applications, engineers, graduate students as well as researchers in numerical analysis.
Introduction To Reaction Diffusion Equations
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Author : King-Yeung Lam
language : en
Publisher: Springer Nature
Release Date : 2022-12-01
Introduction To Reaction Diffusion Equations written by King-Yeung Lam and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-01 with Mathematics categories.
This book introduces some basic mathematical tools in reaction-diffusion models, with applications to spatial ecology and evolutionary biology. It is divided into four parts. The first part is an introduction to the maximum principle, the theory of principal eigenvalues for elliptic and periodic-parabolic equations and systems, and the theory of principal Floquet bundles. The second part concerns the applications in spatial ecology. We discuss the dynamics of a single species and two competing species, as well as some recent progress on N competing species in bounded domains. Some related results on stream populations and phytoplankton populations are also included. We also discuss the spreading properties of a single species in an unbounded spatial domain, as modeled by the Fisher-KPP equation. The third part concerns the applications in evolutionary biology. We describe the basic notions of adaptive dynamics, such as evolutionarily stable strategies and evolutionary branching points, in the context of a competition model of stream populations. We also discuss a class of selection-mutation models describing a population structured along a continuous phenotypical trait. The fourth part consists of several appendices, which present a self-contained treatment of some basic abstract theories in functional analysis and dynamical systems. Topics include the Krein-Rutman theorem for linear and nonlinear operators, as well as some elements of monotone dynamical systems and abstract competition systems. Most of the book is self-contained and it is aimed at graduate students and researchers who are interested in the theory and applications of reaction-diffusion equations.
Optimal Control And Viscosity Solutions Of Hamilton Jacobi Bellman Equations
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Author : Martino Bardi
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-05-21
Optimal Control And Viscosity Solutions Of Hamilton Jacobi Bellman Equations written by Martino Bardi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-21 with Science categories.
The purpose of the present book is to offer an up-to-date account of the theory of viscosity solutions of first order partial differential equations of Hamilton-Jacobi type and its applications to optimal deterministic control and differential games. The theory of viscosity solutions, initiated in the early 80's by the papers of M.G. Crandall and P.L. Lions [CL81, CL83], M.G. Crandall, L.C. Evans and P.L. Lions [CEL84] and P.L. Lions' influential monograph [L82], provides an - tremely convenient PDE framework for dealing with the lack of smoothness of the value functions arising in dynamic optimization problems. The leading theme of this book is a description of the implementation of the viscosity solutions approach to a number of significant model problems in op- real deterministic control and differential games. We have tried to emphasize the advantages offered by this approach in establishing the well-posedness of the c- responding Hamilton-Jacobi equations and to point out its role (when combined with various techniques from optimal control theory and nonsmooth analysis) in the important issue of feedback synthesis.
Mean Field Game And Its Applications In Wireless Networks
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Author : Reginald A. Banez
language : en
Publisher: Springer Nature
Release Date : 2021-10-30
Mean Field Game And Its Applications In Wireless Networks written by Reginald A. Banez and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-30 with Computers categories.
This book covers the basic theory of mean field game (MFG) and its applications in wireless networks. It starts with an overview of the current and future state-of-the-art in 5G and 6G wireless networks. Then, a tutorial is presented for MFG, mean-field-type game (MFTG), and prerequisite fields of study such as optimal control theory and differential games. This book also includes a literature survey of MFG-based research in wireless network technologies such as ultra-dense networks (UDNs), device-to-device (D2D) communications, internet-of-things (IoT), unmanned aerial vehicles (UAVs), and mobile edge networks (MENs). Several applications of MFG and MFTG in UDNs, social networks, and multi-access edge computing networks (MECNs) are introduced as well. Applications of MFG covered in this book are divided in three parts. The first part covers three single-population MFG research works or case studies in UDNs including ultra-dense D2D networks, ultra-dense UAV networks, and dense-user MECNs. The second part centers on a multiple-population MFG (MPMFG) modeling of belief and opinion evolution in social networks. It focuses on a recently developed MPMFG framework and its application in analyzing the behavior of users in a multiple-population social network. Finally, the last part concentrates on an MFTG approach to computation offloading in MECN. The computation offloading algorithms are designed for energy- and time-efficient offloading of computation-intensive tasks in an MECN. This book targets advanced-level students, professors, researchers, scientists, and engineers in the fields of communications and networks. Industry managers and government employees working in these same fields will also find this book useful.
Stochastic And Differential Games
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Author : Martino Bardi
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Stochastic And Differential Games written by Martino Bardi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The theory of two-person, zero-sum differential games started at the be ginning of the 1960s with the works of R. Isaacs in the United States and L.S. Pontryagin and his school in the former Soviet Union. Isaacs based his work on the Dynamic Programming method. He analyzed many special cases of the partial differential equation now called Hamilton Jacobi-Isaacs-briefiy HJI-trying to solve them explicitly and synthe sizing optimal feedbacks from the solution. He began a study of singular surfaces that was continued mainly by J. Breakwell and P. Bernhard and led to the explicit solution of some low-dimensional but highly nontriv ial games; a recent survey of this theory can be found in the book by J. Lewin entitled Differential Games (Springer, 1994). Since the early stages of the theory, several authors worked on making the notion of value of a differential game precise and providing a rigorous derivation of the HJI equation, which does not have a classical solution in most cases; we mention here the works of W. Fleming, A. Friedman (see his book, Differential Games, Wiley, 1971), P.P. Varaiya, E. Roxin, R.J. Elliott and N.J. Kalton, N.N. Krasovskii, and A.I. Subbotin (see their book Po sitional Differential Games, Nauka, 1974, and Springer, 1988), and L.D. Berkovitz. A major breakthrough was the introduction in the 1980s of two new notions of generalized solution for Hamilton-Jacobi equations, namely, viscosity solutions, by M.G. Crandall and P.-L.
College Of Engineering
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Author : University of Michigan. College of Engineering
language : en
Publisher: UM Libraries
Release Date : 1990
College Of Engineering written by University of Michigan. College of Engineering and has been published by UM Libraries this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Engineering schools categories.