01073nas a2200121   4500008004300000245008500043210006900128260002100197520064400218100002800862700002500890856003600915       2007                        en_Ud  00aViscosity solutions of Hamilton-Jacobi equations with discontinuous coefficients0 aViscosity solutions of HamiltonJacobi equations with discontinuo  bWorld Scientific3 aWe consider Hamilton--Jacobi equations, where the Hamiltonian depends discontinuously on both the spatial and temporal location. Our main results are the existence and well--posedness of a viscosity solution to the Cauchy problem. We define a viscosity solution by treating the discontinuities in the coefficients analogously to \\\"internal boundaries\\\". By defining an appropriate penalization function, we prove that viscosity solutions are unique. The existence of viscosity solutions is established by showing that a sequence of front tracking approximations is compact in $L^\\\\infty$, and that the limits are viscosity solutions.1 aCoclite, Giuseppe Maria1 aRisebro, Nils Henrik  uhttp://hdl.handle.net/1963/2907