We prove a general convergence result for singular perturbations with an arbitrary number of scales of fully nonlinear degenerate parabolic PDEs. As a special case we cover the iterated homogenization for such equations with oscillating initial data. Explicit examples, among others, are the two-scale homogenization of quasilinear equations driven by a general hypoelliptic operator and the n-scale homogenization of uniformly parabolic fully nonlinear PDEs.
We consider periodic homogenization of the fully nonlinear uniformly elliptic equationWe give an estimate of the rate of convergence of u ε to the solution u of the homogenized problem u + H x, Du, D 2 u = 0. Moreover we describe a numerical scheme for the approximation of the effective nonlinearity H and we estimate the corresponding rate of convergence.
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Three definitions of viscosity solutions for Hamilton–Jacobi equations on networks recently appeared in literature (Achdou et al. (2013) [1], Imbert et al. (2013) [4], Schieborn and Camilli (2013) [6]). Being motivated by various applications, they appear to be considerably different. The aim of this note is to establish their equivalence
In [14], Guéant, Lasry and Lions considered the model problem "What time does meeting start?" as a prototype for a general class of optimization problems with a continuum of players, called Mean Field Games problems. In this paper we consider a similar model, but with the dynamics of the agents defined on a network. We discuss appropriate transition conditions at the vertices which give a well posed problem and we present some numerical results
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