(untitled) (Prosiding Seminar Nasional Matematika dan Pendidikan Matematika, 2022)
The study of viscosity solution to Hamilton-Jacobi equation was attracted researchers in the last decades. The study focused on completing the question regarding existence, uniqueness, and regularity of the solution. In this research, we covered the existence of viscosity solutions to the ergodic problem or Hamilton-Jacobi equation of contact type in the n-dimension with some general assumptions. The viscosity solutions obtained are not unique in general. A prototype of the Hamiltonian class was investigated and analyzed to show the problem the uniqueness of the viscosity solution. We used the method in Jing (2020:6) to obtain the existence and uniqueness of the ergodic problem.