Approximation of Hamilton Jacobi equations on irregular data (Paperback)


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.

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Product Description

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.

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Product Details

General

Imprint

Lap Lambert Academic Publishing

Country of origin

Germany

Release date

May 2012

Availability

Expected to ship within 10 - 15 working days

First published

May 2012

Authors

Dimensions

229 x 152 x 8mm (L x W x T)

Format

Paperback - Trade

Pages

128

ISBN-13

978-3-659-14053-2

Barcode

9783659140532

Categories

LSN

3-659-14053-8



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