Asymptotic Solutions of Hamilton-Jacobi Equations with State Constraints

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Viscosity solutions of general viscous Hamilton–Jacobi equations (2013, methodology): “[19] H. Mitake.”
On the Large Time Behavior of Solutions of Hamilton–Jacobi Equations Associated with Nonlinear Boundary Conditions (2011, background): “The third author [27] studied the case of the state constraint boundary condition and then the Dirichlet boundary conditions [28, 29].”
Long-time Behavior of Solutions of Hamilton–Jacobi Equations with Convex and Coercive Hamiltonians (2009, methodology): “We refer to the literatures [3, 5, 8, 9, 10, 20 , 21, 22, 23] and references therein for more details.”
An Introduction to the Theory of Viscosity Solutions for First-Order Hamilton–Jacobi Equations and Applications (2013, background): “Mitake [38] studied the case of the state constraint boundary condition and then the Dirichlet boundary conditions [39, 40].”