双曲-椭圆耦合方程组初边值问题解的渐近性态

Asymptotic Behaviors of Solutions for the Initial Boundary Problem of Hyperbolic-Elliptic Coupled Systems

研究双曲椭圆耦合方程组ut+f(u)x+qx=0,-qxx+q+ux=0的初边值问题,其初始值满足u(x,0)=u0(x)→u+(x→∞),u+>0且u0(0)=0,边界满足u(0,t)=0.在流函数f满足f'(0)=f(0)=0,f″>0及初值为小扰动的条件下,用L2能量方法证明其解的整体存在性和渐近收敛于弱稀疏波.

This paper is concerned with the initial-boundary value problem for the hyperbolic-elliptic coupled system ut＋f（u）x＋qx=0,-qxx＋q＋ux=0 with the initial date satisfying u（x,0）=u0（x）→u＋（x→∞）,u＋ 0 and u0（0）=0,and the boundary condition u（0,t）=0.Under the conditions that the flux function f′（0）=f（0）=0,f″0,we prove that the global solution exists and converges time-asymptotically to a weak rarefaction wave for the small initial disturbance by using of an L^2 energy method.