Viscosity solutions of contact Hamilton-Jacobi equations with Hamiltonians depending periodically on unknown functions
Published in Communications on Pure and Applied Analysis, 2023
Recommended citation: P. Ni, K. Wang and J. Yan, Viscosity solutions of contact Hamilton-Jacobi equations with Hamiltonians depending periodically on unknown functions, Comm. Pure Appl. Anal., 22 (2023), 668-685. https://www.aimsciences.org//article/doi/10.3934/cpaa.2023005
This paper is about H-J equations with the Hamiltonian periodic in the unknown function. We proved that the set C of all cās such that
H(x,Du(x),u(x))=c
has viscosity solutions is a compact interval. We also proved that the solutions of
ā_t u(x,t)+H(x,ā_x u(x,t),u(x,t))=c
is uniformly bounded and equi-Lipschitz continuous for all c in C.
Recommended citation: P. Ni, K. Wang and J. Yan, Viscosity solutions of contact Hamilton-Jacobi equations with Hamiltonians depending periodically on unknown functions, Comm. Pure Appl. Anal., 22 (2023), 668-685.