Exit-Time of Granular Media Equation Starting in a Local Minimum

. We are interested in a nonlinear partial differential equation: the granular media one. Thanks to some of our previous results [10, 11], we know that under easily checked assumptions, there is a unique steady state. We point out that we consider a case in which the con(cid:12)ning potential is not globally convex. According to recent articles [8, 9], we know that there is weak convergence towards this steady state. However, we do not know anything about the rate of convergence. In this paper, we make a (cid:12)rst step to this direction by proving a deterministic Kramers’type law concerning the (cid:12)rst time that the solution of the granular media equation leaves a local well. In other words, we show that the solution of the granular media equation is trapped around a local minimum during a time exponentially equivalent to exp { 2 (cid:27) 2 H } , H being the so-called exit-cost.