带松弛项的粘性双曲系统解的渐近状态

带松弛项的粘性双曲系统解的渐近状态 The Asymptotic Behavior of Hyperbolic System with Relaxation and Viscosity 徐红梅 XU Hong-mei 1 first-author 武汉大学数学与统计学院,湖北,武汉,430072 武汉大学数学与统计学院,湖北,武汉,430072 School of Mathematics and Statistics, Wuhan University School of Mathematics and Statistics, Wuhan University 考虑带松弛项的粘性系统ut+vx=εuxxvt+ux=αu-vτ+εvxx,当松驰因子τ→0时的解的渐近状态,先算出本方程的格林函数,然后由Duhamel原理得到解的精确表达式,通过对格林函数的逐点估计,得到当α2<ετ+1时,此方程组的解趋近于一个以α为速度的行波解,否则当τ→0时,不可能得到能作Fourier变换的解. We consider the asymptotic behavior of system u t +v x =εu x xv t +u x =αu-vτ+εv x x when relaxation factor τ→0. Through the pointwise estimate of the Green function, we obtain explicit expressions of the time-asymptotic behavior of the solution. We get the result that the solution approaches to a wave solution with speed α when α 2 < ετ+1. 松弛项 粘性项 解的渐近状态 relaxation viscosity asymptotic behavior O302 武汉大学科技创新基金资助项目 2004-01-01 2021-04-01 1