Download or read book Hamilton Jacobi Equations Theory and Applications written by Hung Vinh Tran and published by American Mathematical Soc.. This book was released on 2021-09-17 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Hamilton Jacobi Equations Approximations Numerical Analysis and Applications written by Yves Achdou and published by Springer. This book was released on 2013-05-24 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
Download or read book Semiconcave Functions Hamilton Jacobi Equations and Optimal Control written by Piermarco Cannarsa and published by Springer Science & Business Media. This book was released on 2007-12-31 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: * 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
Download or read book On Modern Approaches of Hamilton Jacobi Equations and Control Problems with Discontinuities written by Guy Barles and published by Springer Nature. This book was released on 2024-01-30 with total page 569 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Hamilton Jacobi Equation A Global Approach written by Benton and published by Academic Press. This book was released on 1977-06-29 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hamilton-Jacobi Equation: A Global Approach
Download or read book The Hamilton Jacobi Theory in the Calculus of Variations written by Hanno Rund and published by Krieger Publishing Company. This book was released on 1966 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Semi Lagrangian Approximation Schemes for Linear and Hamilton Jacobi Equations written by Maurizio Falcone and published by SIAM. This book was released on 2014-01-31 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Optimal Control and Viscosity Solutions of Hamilton Jacobi Bellman Equations written by Martino Bardi and published by Springer Science & Business Media. This book was released on 2009-05-21 with total page 588 pages. Available in PDF, EPUB and Kindle. Book excerpt: This softcover book is a self-contained account of the theory of viscosity solutions for first-order partial differential equations of Hamilton–Jacobi type and its interplay with Bellman’s dynamic programming approach to optimal control and differential games. It will be of interest to scientists involved in the theory of optimal control of deterministic linear and nonlinear systems. The work may be used by graduate students and researchers in control theory both as an introductory textbook and as an up-to-date reference book.
Download or read book Constrained Hamilton Jacobi Equations and Further Applications Via Optimal Control Theory written by Yeon Eung Kim and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation, two research directions are presented. The first direction is on the study of the constrained Hamilton-Jacobi equation \begin{equation*} \begin{cases} u_t=H(Du)+R(x, I(t)) & \text{in }\R^n \times (0,\infty), \\ \sup_{\R^n} u(\cdot, t)=0 & \text{on }[0,\infty), \end{cases} \end{equation*} with initial conditions $I(0)=I_0>0$, $u(x,0)=u_0(x)$ on $\R^n$. Here $(u, I)$ is a pair of unknowns and a Hamiltonian $H$ and a reaction term $R$ are given. Moreover, $I(t)$ is an unknown constraint (Lagrange multiplier) that constrains the supremum of $u$ to be always zero. We construct a solution in the viscosity setting using the fixed point argument when the reaction term $R(x, I)$ is strictly decreasing in $I$. We also discuss both uniqueness and nonuniqueness. For uniqueness, a certain structural assumption on $R(x, I)$ is needed. We also provide an example with infinitely many solutions when the reaction term is not strictly decreasing in $I$. Furthermore, the uniqueness of a pair $(u, I)$ is achieved for one-dimensional case using the optimal control formula. The second direction is based on joint work with H. Tran and S. Tu is concerned with rate of convergence of viscosity solutions to state-constraint Hamilton-Jacobi equations defined in nested domains. In particular, we consider a sequence of balls $\{ B_k\}_{k \in \N}$ in $\R^n$ for the domain where a ball centered at the origin with radius $k$ is denoted by $B_k$. We obtain rate of convergence of $u_k$ which is a solution to the state-constraint problem in $B_k$, to $u$ which is a solution to the corresponding problem in $\R^n$ using the optimal control formula. The rate we obtain is indeed optimal.
Download or read book Dynamical and Geometric Aspects of Hamilton Jacobi and Linearized Monge Amp re Equations written by Hiroyoshi Mitake and published by Springer. This book was released on 2017-06-14 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Partial Differential Equations Of First Order And Their Applications To Physics 2nd Edition written by Lopez Velazquez Gustavo and published by World Scientific Publishing Company. This book was released on 2012-03-21 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Hamilton Jacobi Equations in Hilbert Spaces written by Viorel Barbu and published by Pitman Advanced Publishing Program. This book was released on 1983 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: This presents a self-contained treatment of Hamilton-Jacobi equations in Hilbert spaces. Most of the results presented have been obtained by the authors. The treatment is novel in that it is concerned with infinite dimensional Hamilton-Jacobi equations; it therefore does not overlap with Research Note #69. Indeed, these books are in a sense complementary.
Download or read book Special Issue Hamilton Jacobi Equations and Related Topics written by Martino Bardi and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Jacobi s Lectures on Dynamics written by A. Clebsch and published by Springer. This book was released on 2009-08-15 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: The name of C. G. J. Jacobi is familiar to every student of mathematics, thanks to the Jacobion determinant, the Hamilton-Jacobi equations in dynamics, and the Jacobi identity for vector fields. Best known for his contributions to the theory of elliptic and abelian functions, Jacobi is also known for his innovative teaching methods and for running the first research seminar in pure mathematics. A record of his lectures on Dynamics given in 1842-43 at Konigsberg, edited by A. Clebsch, has been available in the original German. This is an English translation. It is not just a historical document; the modern reader can learn much about the subject directly from one of its great masters.
Download or read book Partial Differential Equations of First Order and Their Applications to Physics written by Gustavo López and published by World Scientific Publishing Company. This book was released on 1999-12-16 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Hamiltonian Dynamical Systems and Applications written by Walter Craig and published by Springer Science & Business Media. This book was released on 2008-02-17 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the collected and extended notes from the lectures on Hamiltonian dynamical systems and their applications that were given at the NATO Advanced Study Institute in Montreal in 2007. Many aspects of the modern theory of the subject were covered at this event, including low dimensional problems. Applications are also presented to several important areas of research, including problems in classical mechanics, continuum mechanics, and partial differential equations.
Download or read book Viscosity Solutions and Applications written by Martino Bardi and published by Springer. This book was released on 2006-11-13 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume comprises five extended surveys on the recent theory of viscosity solutions of fully nonlinear partial differential equations, and some of its most relevant applications to optimal control theory for deterministic and stochastic systems, front propagation, geometric motions and mathematical finance. The volume forms a state-of-the-art reference on the subject of viscosity solutions, and the authors are among the most prominent specialists. Potential readers are researchers in nonlinear PDE's, systems theory, stochastic processes.
