A selection principle for viscosity solutions of degenerate viscous Hamilton-Jacobi equations is derived via nonlinear adjoint methods, yielding uniform convergence to any desired ergodic solution expressed through generalized Mather measures and the potential.
Convergence/divergence phenomena in the vanishing discount limit of Hamilton-Jacobi equations.Preprint
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For inhomogeneous discounted HJ equations on closed manifolds, viscosity solutions exist and are asymptotically stable precisely when the constant exceeds a critical value c0, with convergence rates determined by integrals of the discount factor over Mather measures.
PDE criteria based on the critical value of the Hamiltonian and viscosity subsolutions determine Lyapunov stability and instability for stationary solutions of contact-type Hamilton-Jacobi equations with continuous convex coercive Hamiltonians.
citing papers explorer
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A new selection problem for degenerate viscous Hamilton-Jacobi equations
A selection principle for viscosity solutions of degenerate viscous Hamilton-Jacobi equations is derived via nonlinear adjoint methods, yielding uniform convergence to any desired ergodic solution expressed through generalized Mather measures and the potential.
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On the inhomogeneous discounted Hamilton-Jacobi equations
For inhomogeneous discounted HJ equations on closed manifolds, viscosity solutions exist and are asymptotically stable precisely when the constant exceeds a critical value c0, with convergence rates determined by integrals of the discount factor over Mather measures.
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A PDE formulation of Lyapunov stability for contact-type Hamilton-Jacobi equations
PDE criteria based on the critical value of the Hamiltonian and viscosity subsolutions determine Lyapunov stability and instability for stationary solutions of contact-type Hamilton-Jacobi equations with continuous convex coercive Hamiltonians.