Results 1 
5 of
5
STOCHASTIC HOMOGENIZATION OF INTERFACES MOVING WITH CHANGING SIGN VELOCITY
"... Abstract. 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 HamiltonJacobi equation with a positively homogeneous no ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
Abstract. 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 HamiltonJacobi equation with a positively homogeneous noncoercive 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 HamiltonJacobi equation converge in Lāweak ā 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.
DETERMINISTIC WALK IN AN EXCITED RANDOM ENVIRONMENT
"... Abstract. Deterministic walk in an excited random environment is a nonMarkov integervalued process (Xn) n=0, whose jump at time n depends on the number of visits to the site Xn. The environment can be understood as stacks of cookies on each site of Z. Once all cookies are consumed at a given site, ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. Deterministic walk in an excited random environment is a nonMarkov integervalued process (Xn) n=0, whose jump at time n depends on the number of visits to the site Xn. The environment can be understood as stacks of cookies on each site of Z. Once all cookies are consumed at a given site, every subsequent visit will result in a walk taking a step according to the direction prescribed by the last consumed cookie. If each site has exactly one cookie, then the walk ends in a loop if it ever visits the same site twice. If the number of cookies per site is increased to two, the walk can visit a site infinitely many times and still not end in a loop. Nevertheless the moments of Xn are sublinear in n and we establish monotonicity results on the environment that imply large deviations. 1.
LARGE TIME AVERAGE OF REACHABLE SETS AND APPLICATIONS TO HOMOGENIZATION OF INTERFACES MOVING WITH OSCILLATORY SPATIOTEMPORAL VELOCITY
, 2014
"... ..."