CAJ | 학술논문

主要考虑下面的交通模型的行波解的渐近稳定性.{vt-ux=0 (E)ut+p(v)x=1/ε(f(v)-u+μuxx 其中初始值为 (v,u)(x,0)=(v0(x),u0(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.
주요고필하면적교통모형적행파해적점근은정성.{vt-ux=0 (E)ut+p(v)x=1/ε(f(v)-u+μuxx 기중초시치위 (v,u)(x,0)=(v0(x),u0(x))→(v±,u±),v±＞0,as x→±∞.(Ⅰ)재윤허류함수f불시요함수이급초시치재무궁원처적겁한불만족평형방정적조건하,아문득도료은정성정리.증명적방법주요시통과구조일대오차함수이급운용가권능량고계판법.
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 (E)ut + p(v)x = 1/ε(f(v) - u) + μuxxwith initial data (v,u)(x,0) = (v0(x),u0(x)) → (v±,u±),v±＞ 0, as x →±∞. (Ⅰ)Stability theorem is obtained in the absence of the concavity of the flux function f and in the allowance 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.