廣義BBMB方程初值與邊界值問題之研究

An Initial-And Boundary-Value Problem for the Generalized Benjamin-Mahony-Burgers Equation

左太政(Tai-Cheng Tso)

《高雄師大學報》 18期 (2005/06) Pp. 265-284

https://doi.org/10.7060/KNUJ.200506.0265

摘要

本文主要研究廣義Benjamin-Bona-Mahony-Burgers方程（簡稱廣義BBMB方程）
u1+u(上標 p)u(下標 x)-α^2u(下標 xxt)-νu(下標 xx)=0, P≥l, x∈[0,1], t≥0.
當初值及邊界值條件為
u(x, 0)=f(x), 0≤x≤1,
u(0, t)=h(t), u(1, t)=g(t), t≥0,
探討其解的存在性與唯一性，其中α≥0及ν≥0皆為常數。其次，我們也證明解的連續相依性質。

關鍵字

初值及邊界值問題 ； BBMB方程 ； 連續相依性質

並列摘要

The aim of this paper is to study the existence arid uniqueness of the solution of an initial- and boundary-value problem for the generalized Benjamin-Bona-Mahony-Burgers equation (GBBMB for short)
u(subscript t)u(superscript p)ux-α^2u(subscript xxt)-υu(subscript xx)=0, P≥l, x∈[0,1], t≥0
with the conditions
u(x, 0)=f(x), 0≤x≤1,
u(0,t)=h(t), u(1,t)=g(t), t≥0,
where α≥0 and υ≥0 are constants. We also prove the continuous dependence of these solutions on variations of the specified data within appropriate function spaces.

並列關鍵字

initial-and boundary-value problem ； the Benjamin-Bona-Mahony-Burgers equation ； continuous dependence