Stochastic homogenization of interfaces moving with changing sign velocity

Adina Ciomaga (1) , Panagiotis E. Souganidis (1) , Hung V. Tran (1)

1 Department of Mathematics [Chicago]

We are interested in the averaged behavior of interfaces moving in stationary ergodic environments, with oscillatory normal velocity which changes sign. This problem can be reformulated, using level sets, as the homogenization of a Hamilton-Jacobi equation with a positively homogeneous non-coercive Hamiltonian. The periodic setting was earlier studied by Cardaliaguet, Lions and Souganidis (2009). Here we concentrate in the random media and show that the solutions of the oscillatory Hamilton-Jacobi equation converge in $L^\infty$-weak $*$ to a linear combination of the initial datum and the solutions of several initial value problems with deterministic effective Hamiltonian(s), determined by the properties of the random media.

Mots clés: front propagation; stochastic homogenization; Hamilton-Jacobi equations; viscosity solutions; non-coercive Hamiltonian; random media; level sets; front propagation.

Domaines: Mathématiques générales [math.GM]

Adina Ciomaga, Panagiotis E. Souganidis, Hung V. Tran. Stochastic homogenization of interfaces moving with changing sign velocity. Calculus of Variations and Partial Differential Equations, 2014, 50 (1-2), pp.283-304. ⟨10.1007/s00526-013-0636-2⟩. ⟨hal-00969113⟩