Approximation of Hamilton Jacobi Equations on Irregular Data

Released on by Adriano Festa
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  • Approximation of Hamilton Jacobi Equations on Irregular Data Book Detail

  • Author : Adriano Festa
  • Release Date : 2012-05
  • Publisher : LAP Lambert Academic Publishing
  • Genre :
  • Pages : 128
  • ISBN 13 : 9783659140532
  • File Size : 99,99 MB
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Approximation of Hamilton Jacobi Equations on Irregular Data by Adriano Festa PDF Summary

Book 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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