Explicit Hopf-Lax type formulas for Hamilton-Jacobi equations and conservation laws with discontinuous coefficients (Q2383025)

The paper is concerned with the study of a Hamilton-Jacobi equation with Hamiltonian that is discontinuous in the space variable. The authors characterize some infinite classes of solutions in terms of explicit Hopf-Lax type formulas which are obtained from the viscosity solutions of the corresponding Hamilton-Jacobi equation with discontinuous Hamiltonian. The concept of generalized Rankine-Hugoniot condition is introduced and prove the existence and uniqueness.