Inserted: 16 jun 2018
Last Updated: 6 aug 2019
Journal: Proc. Roy. Soc. Edinburgh Sect. A
This paper deals with the periodic homogenization of nonlocal parabolic Hamilton-Jacobi equations with superlinear growth in the gradient terms. We show that the problem presents different features depending on the order of the nonlocal operator, giving rise to three different cell problems and effective operators. To prove the locally uniform convergence to the unique solution of the Cauchy problem for the effective equation we need a new comparison principle among viscosity semi-solutions of integro-differential equations that can be of independent interest.
Keywords: Homogenization, Viscosity solutions, Hamilton-Jacobi equations, Comparison principle, integro-differential equations, fractional Laplacians