Approximation of Hamilton Jacobi Equations on Irregular Data: Semilagrangian Methods and Convergence in Some Non Classical Situations - Adriano Festa - Bøger - LAP LAMBERT Academic Publishing - 9783659140532 - 26. maj 2012
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Approximation of Hamilton Jacobi Equations on Irregular Data: Semilagrangian Methods and Convergence in Some Non Classical Situations

Adriano Festa

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Approximation of Hamilton Jacobi Equations on Irregular Data: Semilagrangian Methods and Convergence in Some Non Classical Situations

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.

Medie Bøger     Paperback Bog   (Bog med blødt omslag og limet ryg)
Udgivet 26. maj 2012
ISBN13 9783659140532
Forlag LAP LAMBERT Academic Publishing
Antal sider 128
Mål 150 × 8 × 226 mm   ·   209 g
Sprog Tysk