A remark on the large-time behavior of solutions to Burgers-Poisson equations

Abstract

We study large-time behavior of solutions to the initial-value problem for the Burgers-Poisson equations introduced to analyze the behavior of high-temperature gas. It is known that the solution tends to a solution to the viscous Burgers equation. By a suitable choice of a linearized equation including the low-order term, we succeed in improving the asymptotic rate.