On the critical amplitudes of acceleration wave to shock wave transition in white noise random media (Q1309435)

The problem of transition of acceleration waves into shock waves is addressed in the context of weakly random media. A class of random media is modeled by a vector white noise random process representing two material coefficients appearing in the Bernoulli equation governing the evolution of acceleration waves. The problem of shock formation, which involves a stochastic competition of dissipation and elastic nonlinearity, is treated using a diffusion formulation for the Markov process of the inverse amplitude.