Title
Approximation of Hamilton Jacobi equations on irregular data: semiLagrangian methods and convergence in some non classical situa,Used
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This book deals with the development and the analysis of numerical methods for the resolution of first order nonlinear differential equations of HamiltonJacobi type on irregular data. These equations arises for example in the study of front propagation via the level set methods, the ShapefromShading problem and, in general, in Control theory. Our contribution to the numerical approximation of HamiltonJacobi 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 HamiltonJacobi 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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