부산대학교 도서관

In this paper the authors study the large time behaviour of solutions of a non-local regularisation of the inviscid Burgers equation. They prove that the long-time asymptotic profile of the solution is the $N$-wave entropy solution of the inviscid Burgers equation, when the initial datum is non-negative, bounded and integrable. The convergence is done in $L^p$ norm for $1\leq p<\infty$. The main ingredients of the proof are a scaling argument and a non-local Oleinik-type estimate. The result is also illustrated by several numerical simulations. The concluding section contains several open problems.