具有非凸条件的阻尼波动方程的一般初边值问题解的渐近性态

Asymptotic behaviors of solutions of an initial-boundary value problem for damped wave equation with non-convexity

在一维半空间中,研究具有一般边界的阻尼波动方程的解收敛到稳定波的渐近性态.在流函数为非凸和初边值为小扰动的条件下,证明了其解的整体存在性及解渐近收敛到相应的稳定波.证明过程采用L2-加权能量方法.

Asymptotic behaviors of solutions for the damped wave equation with a general boundary data in a half space is concerned. Under the condition of non-convex flux and small perturbation for the initial data, the global solutions exist and converge The proof is given by a L^2-weighted energy method. time-asymptotically to a stationary wave is proved.