Stochastic homogenization of some interface propagation problems.

Summary In this work, we study the homogenization of some front propagation problems in stationary and ergodic environments. In the first part, we study the stochastic homogenization of some non-local front propagation problems. In particular, a non-local version of the perturbed Evans test function method is given. The second part is devoted to the numerical approximation of the effective Hamiltonian which follows from the stochastic homogenization of the Hamilton-Jacobi equations. Error estimates between the numerical solutions and the effective Hamiltonian are established. In the third part, we are interested in the stochastic homogenization of problems of propagating fronts which evolve in the normal direction with a speed which can be unbounded. We show homogenization results in the case of i.i.d. media.