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Approximation of Hamilton Jacobi Equations on Irregular Data

2012-05
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Release : 2012-05
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Kind : eBook
Book Rating : 532/5 ( reviews)

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Book Synopsis Approximation of Hamilton Jacobi Equations on Irregular Data by : Adriano Festa

Download or read book Approximation of Hamilton Jacobi Equations on Irregular Data written by Adriano Festa. This book was released on 2012-05. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the development and the analysis of numerical methods for the resolution of first order nonlinear differential equations of Hamilton-Jacobi type on irregular data. These equations arises for example in the study of front propagation via the level set methods, the Shape-from-Shading problem and, in general, in Control theory. Our contribution to the numerical approximation of Hamilton-Jacobi equations consists in the proposal of some semiLagrangian schemes for different kind of discontinuous Hamiltonian and in an analysis of their convergence and a comparison of the results on some test problems. In particular we will approach with an eikonal equation with discontinuous coefficients in a well posed case of existence of Lipschitz continuous solutions. Furthermore, we propose a semiLagrangian scheme also for a Hamilton-Jacobi equation of a eikonal type on a ramified space, for example a graph. This is a not classical domain and only in last years there are developed a systematic theory about this. We present, also, some applications of our results on several problems arise from applied sciences.

Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications

2013-05-24 Mathematics
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Release : 2013-05-24
Genre : Mathematics
Kind : eBook
Book Rating : 330/5 ( reviews)

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Book Synopsis Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications by : Yves Achdou

Download or read book Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications written by Yves Achdou. This book was released on 2013-05-24. 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).

Hamilton-Jacobi Equation: A Global Approach

1977-06-29 Computers
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Release : 1977-06-29
Genre : Computers
Kind : eBook
Book Rating : 408/5 ( reviews)

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Book Synopsis Hamilton-Jacobi Equation: A Global Approach by : Benton

Download or read book Hamilton-Jacobi Equation: A Global Approach written by Benton. This book was released on 1977-06-29. Available in PDF, EPUB and Kindle. Book excerpt: Hamilton-Jacobi Equation: A Global Approach

Dynamical and Geometric Aspects of Hamilton-Jacobi and Linearized Monge-Ampère Equations

2017-06-14 Mathematics
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Release : 2017-06-14
Genre : Mathematics
Kind : eBook
Book Rating : 087/5 ( reviews)

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Book Synopsis Dynamical and Geometric Aspects of Hamilton-Jacobi and Linearized Monge-Ampère Equations by : Hiroyoshi Mitake

Download or read book Dynamical and Geometric Aspects of Hamilton-Jacobi and Linearized Monge-Ampère Equations written by Hiroyoshi Mitake. This book was released on 2017-06-14. 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.

Approximation Schemes for Viscosity Solutions of Hamilton-Jacobi Equations

1983 Hamilton-Jacobi equations
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Release : 1983
Genre : Hamilton-Jacobi equations
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Book Synopsis Approximation Schemes for Viscosity Solutions of Hamilton-Jacobi Equations by : Panagiotis E. Souganidis

Download or read book Approximation Schemes for Viscosity Solutions of Hamilton-Jacobi Equations written by Panagiotis E. Souganidis. This book was released on 1983. Available in PDF, EPUB and Kindle. Book excerpt: Equations of Hamilton-Jacobi type arise in many areas of application, including the calculus of variations of variations, control theory and differential games. Recently Crandall and Lions established the correct notion of generalized solutions for these equations. This article discusses the convergence of general approximation schemes to this solution and gives, under certain hypotheses, explicit error estimates. These results are then applied to obtain various representations. These include max-min representations of solutions relevant to the theory of differential games (which imply the existence of the value of the game), representations as limits of solutions of general explicit and implicit finite difference schemes, and as limits of several types of Trotter products. (Author).

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