Viscosity Solutions And Applications

Author : Nikos Katzourakis
Publisher : Springer
Page : 123 pages
File Size : 50,5 Mb
Release : 2014-11-26
Category : Mathematics
ISBN : 9783319128290

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An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L∞ by Nikos Katzourakis Pdf

The purpose of this book is to give a quick and elementary, yet rigorous, presentation of the rudiments of the so-called theory of Viscosity Solutions which applies to fully nonlinear 1st and 2nd order Partial Differential Equations (PDE). For such equations, particularly for 2nd order ones, solutions generally are non-smooth and standard approaches in order to define a "weak solution" do not apply: classical, strong almost everywhere, weak, measure-valued and distributional solutions either do not exist or may not even be defined. The main reason for the latter failure is that, the standard idea of using "integration-by-parts" in order to pass derivatives to smooth test functions by duality, is not available for non-divergence structure PDE.

Author : Maurizio Falcone,Charalampos Makridakis
Publisher : World Scientific
Page : 256 pages
File Size : 51,8 Mb
Release : 2001
Category : Mathematics
ISBN : 981279980X

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Numerical Methods for Viscosity Solutions and Applications by Maurizio Falcone,Charalampos Makridakis Pdf

Geometrical optics and viscosity solutions / A.-P. Blanc, G. T. Kossioris and G. N. Makrakis -- Computation of vorticity evolution for a cylindrical Type-II superconductor subject to parallel and transverse applied magnetic fields / A. Briggs ... [et al.] -- A characterization of the value function for a class of degenerate control problems / F. Camilli -- Some microstructures in three dimensions / M. Chipot and V. Lecuyer -- Convergence of numerical schemes for the approximation of level set solutions to mean curvature flow / K. Deckelnick and G. Dziuk -- Optimal discretization steps in semi-lagrangian approximation of first-order PDEs / M. Falcone, R. Ferretti and T. Manfroni -- Convergence past singularities to the forced mean curvature flow for a modified reaction-diffusion approach / F. Fierro -- The viscosity-duality solutions approach to geometric pptics for the Helmholtz equation / L. Gosse and F. James -- Adaptive grid generation for evolutive Hamilton-Jacobi-Bellman equations / L. Grune -- Solution and application of anisotropic curvature driven evolution of curves (and surfaces) / K. Mikula -- An adaptive scheme on unstructured grids for the shape-from-shading problem / M. Sagona and A. Seghini -- On a posteriori error estimation for constant obstacle problems / A. Veeser.

Author : Martino Bardi,Michael G. Crandall,Lawrence C. Evans,Halil M. Soner,Panagiotis E. Souganidis
Publisher : Springer
Page : 268 pages
File Size : 43,9 Mb
Release : 2006-11-13
Category : Mathematics
ISBN : 9783540690436

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Viscosity Solutions and Applications by Martino Bardi,Michael G. Crandall,Lawrence C. Evans,Halil M. Soner,Panagiotis E. Souganidis Pdf

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.

Author : Wendell H. Fleming,Halil Mete Soner
Publisher : Springer Science & Business Media
Page : 436 pages
File Size : 44,8 Mb
Release : 2006-02-04
Category : Mathematics
ISBN : 9780387310718

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Controlled Markov Processes and Viscosity Solutions by Wendell H. Fleming,Halil Mete Soner Pdf

This book is an introduction to optimal stochastic control for continuous time Markov processes and the theory of viscosity solutions. It covers dynamic programming for deterministic optimal control problems, as well as to the corresponding theory of viscosity solutions. New chapters in this second edition introduce the role of stochastic optimal control in portfolio optimization and in pricing derivatives in incomplete markets and two-controller, zero-sum differential games.

Author : Martino Bardi,Italo Capuzzo-Dolcetta
Publisher : Springer Science & Business Media
Page : 588 pages
File Size : 44,6 Mb
Release : 2009-05-21
Category : Science
ISBN : 9780817647551

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Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations by Martino Bardi,Italo Capuzzo-Dolcetta Pdf

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.

Author : Anonim
Publisher : Unknown
Page : 3 pages
File Size : 52,9 Mb
Release : 2006
Category : Electronic
ISBN : OCLC:255947501

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Numerical Methods for Viscosity Solutions and Applications by Anonim Pdf

Author : Maurizio Falcone,Charalampos Makridakis
Publisher : World Scientific
Page : 249 pages
File Size : 53,8 Mb
Release : 2001
Category : Mathematics
ISBN : 9789810247171

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Numerical Methods for Viscosity Solutions and Applications by Maurizio Falcone,Charalampos Makridakis Pdf

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.

Author : Yves Achdou,Guy Barles,Hitoshi Ishii,Grigory L. Litvinov
Publisher : Springer
Page : 316 pages
File Size : 52,8 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 : Luis A. Caffarelli,Xavier Cabré
Publisher : American Mathematical Soc.
Page : 114 pages
File Size : 53,8 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821804377

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Fully Nonlinear Elliptic Equations by Luis A. Caffarelli,Xavier Cabré Pdf

The goal of the book is to extend classical regularity theorems for solutions of linear elliptic partial differential equations to the context of fully nonlinear elliptic equations. This class of equations often arises in control theory, optimization, and other applications. The authors give a detailed presentation of all the necessary techniques. Instead of treating these techniques in their greatest generality, they outline the key ideas and prove the results needed for developing the subsequent theory. Topics discussed in the book include the theory of viscosity solutions for nonlinear equations, the Alexandroff estimate and Krylov-Safonov Harnack-type inequality for viscosity solutions, uniqueness theory for viscosity solutions, Evans and Krylov regularity theory for convex fully nonlinear equations, and regularity theory for fully nonlinear equations with variable coefficients.

Author : Centro internazionale matematico estivo. Session
Publisher : Unknown
Page : 259 pages
File Size : 54,7 Mb
Release : 1997
Category : Electronic
ISBN : OCLC:1132064239

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Viscosity Solutions and Applications by Centro internazionale matematico estivo. Session Pdf

Author : Laurent Decreusefond,Jon Gjerde,Bernt Oksendal,Suleyman Ustunel
Publisher : Springer Science & Business Media
Page : 414 pages
File Size : 51,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461220220

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Stochastic Analysis and Related Topics VI by Laurent Decreusefond,Jon Gjerde,Bernt Oksendal,Suleyman Ustunel Pdf

This volume contains the contributions of the participants of the Sixth Oslo-Silivri Workshop on Stochastic Analysis, held in Geilo from July 29 to August 6, 1996. There are two main lectures " Stochastic Differential Equations with Memory, by S.E.A. Mohammed, " Backward SDE's and Viscosity Solutions of Second Order Semilinear PDE's, by E. Pardoux. The main lectures are presented at the beginning of the volume. There is also a review paper at the third place about the stochastic calculus of variations on Lie groups. The contributing papers vary from SPDEs to Non-Kolmogorov type probabilistic models. We would like to thank " VISTA, a research cooperation between Norwegian Academy of Sciences and Letters and Den Norske Stats Oljeselskap (Statoil), " CNRS, Centre National de la Recherche Scientifique, " The Department of Mathematics of the University of Oslo, " The Ecole Nationale Superieure des Telecommunications, for their financial support. L. Decreusefond J. Gjerde B. 0ksendal A.S. Ustunel PARTICIPANTS TO THE 6TH WORKSHOP ON STOCHASTIC ANALYSIS Vestlia HØyfjellshotell, Geilo, Norway, July 28 -August 4, 1996. E-mail: [email protected] Aureli ALABERT Departament de Matematiques Laurent DECREUSEFOND Universitat Autonoma de Barcelona Ecole Nationale Superieure des Telecom 08193-Bellaterra munications CATALONIA (Spain) Departement Reseaux E-mail: [email protected] 46, rue Barrault Halvard ARNTZEN 75634 Paris Cedex 13 Dept. of Mathematics FRANCE University of Oslo E-mail: [email protected] Box 1053 Blindern Laurent DENIS N-0316 Oslo C.M.I

Author : Hung V. Tran
Publisher : Unknown
Page : 128 pages
File Size : 44,6 Mb
Release : 2021
Category : Electronic books
ISBN : 147046554X

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Hamilton-Jacobi Equations 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 : Daniel Liberzon
Publisher : Princeton University Press
Page : 255 pages
File Size : 40,7 Mb
Release : 2012
Category : Mathematics
ISBN : 9780691151878

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Calculus of Variations and Optimal Control Theory by Daniel Liberzon Pdf

This textbook offers a concise yet rigorous introduction to calculus of variations and optimal control theory, and is a self-contained resource for graduate students in engineering, applied mathematics, and related subjects. Designed specifically for a one-semester course, the book begins with calculus of variations, preparing the ground for optimal control. It then gives a complete proof of the maximum principle and covers key topics such as the Hamilton-Jacobi-Bellman theory of dynamic programming and linear-quadratic optimal control. Calculus of Variations and Optimal Control Theory also traces the historical development of the subject and features numerous exercises, notes and references at the end of each chapter, and suggestions for further study. Offers a concise yet rigorous introduction Requires limited background in control theory or advanced mathematics Provides a complete proof of the maximum principle Uses consistent notation in the exposition of classical and modern topics Traces the historical development of the subject Solutions manual (available only to teachers) Leading universities that have adopted this book include: University of Illinois at Urbana-Champaign ECE 553: Optimum Control Systems Georgia Institute of Technology ECE 6553: Optimal Control and Optimization University of Pennsylvania ESE 680: Optimal Control Theory University of Notre Dame EE 60565: Optimal Control

Author : Martino Bardi,T.E.S. Raghavan,T. Parthasarathy
Publisher : Springer Science & Business Media
Page : 404 pages
File Size : 48,8 Mb
Release : 1999-06
Category : Mathematics
ISBN : 0817640290

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Stochastic and Differential Games by Martino Bardi,T.E.S. Raghavan,T. Parthasarathy Pdf

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.

Author : Maurizio Falcone,Roberto Ferretti
Publisher : SIAM
Page : 331 pages
File Size : 42,8 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.