Singular perturbations of nonlinear degenerate parabolic pDEs: A general convergence result (Q1417413)

The main result of this paper is a general convergence theorem for the viscosity solutions of singularly perturbed problems for fully nonlinear degenerate parabolic equations with highly oscillating initial data. Under the only assumptions that Hamiltonian is ergodic and stabilizing in a suitable sense, the solutions are proved to converge in a relaxed sense to the solution of a limit Cauchy problem with appropriate effective Hamiltonian and initial data. It should reveal a useful tool for studying general singularly perturbed problems by viscosity solutions techniques.