Solution for a System of Hamilton–Jacobi Equations of Special Type and a Link with Nash Equilibrium

Approximation of a Multivalued Solution of the Hamilton-Jacobi Equation

“…Furthermore viscosity approach is equivalent the concept of M-solutions in the following sense: upper (low) envelope of the M-solution is the viscosity supersolution (subsolution) of the Hamilton-Jacobi equations (Lakhtin and Subbotin (1998b)). The Hamilton -Jacobi equations with the discontinuous Hamiltonians have application in optimal control problems, theory of hierarchical systems of the Hamilton-Jacobi equations (Kolpakova (2017)).…”