June 2, 18:00
Professor E.Yu. Panov (Novgorod State University, Veliky Novgorod, Russia).
Title of the talk: On decay of the entropy solution of a scalar conservation law with a perturbed periodic initial function.
We consider the Cauchy problem for a scalar conservation law with an initial function represented as the sum of a periodic function and a function that vanishes at infinity (in the sense of measure). Provided that the flux function is not affine in any semi-vicinity of the mean value of initial data, we establish the long-time decay property of the entropy solution to a constant equal to this mean value. The non-linearity assumption on the flux function is demonstrated to be precise.