For quasilinear hyperbolic systems with time-periodic boundary conditions possessing a dissipative structure, the existence, uniqueness and stability of the time-periodic classical solutions are proved. Moreover, the feedback boundary control with dissipative structure can stabilize the system around the time-periodic solution, provided that the time-periodic boundary conditions are $W^{2,\infty }$ smooth.

中文翻译：

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具有时间周期边界条件的拟线性双曲系统的时间周期解

对于具有耗散结构的时间周期边界条件的拟线性双曲系统，证明了时间周期经典解的存在性，唯一性和稳定性。此外，如果时间周期的边界条件满足，则具有耗散结构的反馈边界控制可以使系统稳定在时间周期解附近。${\mathrm{w\; ^}}^{2，\infty }$ 光滑。