Decay of entropy solutions of a scalar conservation law beyond a stationary ergodic setting (Q2109360)

The authors study the long time behavior of entropy solutions to a scalar conservation law \[ \partial_t u+\operatorname{div}\, f(u)=0 \] with generally random initial data having some ``self-averaging'' properties. Under a standard nondegeneracy condition on the flux the authors establish the long time decay property of entropy solutions in the Besicovitch seminorm. This extends results known in the case of almost periodic initial data.