一个交通模型的行波解的渐近稳定性(英文)

Asymptotic Stability of Traveling Wave Solutions for a Traffic Flow Model

主要考虑下面的交通模型的行波解的渐近稳定性.其中初始值为v_t-u_x=0u_t+p(v)_x=1/ε(f(v))-u)+μu_(xx),(E)(v,u)(x,0)=(v_0(x),u_0(x))→(v_±,u_±),v_±>0,as x→±∞(I)在允许流函数f不是凹函数以及初始值在无穷远处的极限不满足平衡方程的条件下,我们得到了稳定性定理.证明的方法主要是通过构造一对误差函数以及运用加权能量估计办法.

Abstract In this paper, we consider the asymptotic stability of traveling wave solutions with shock profiles for the Cauchy problem for the following traffic flow model {vt-ux=0 ut＋p（v）x=1/ε（f（v）-u）＋μuxx with initial data （v,u）（x,0）=（v0（x）,u0（x））→（v±,u±）,v±〉0,asx→±∞.Stability theorem is obtained in the absence of the concavity of the flux function f and in theallowance of the limits （v±,u±） of the initial data at x=±∞ not satisfying the equilibrium equation, i.e., u±≠ f（v±）. The proofs are given by constructing a pair of correction functions and applying the weighted energy method.