二阶拟线性双曲型方程的精确边界能控性

摘要

本文以二阶拟线性双曲型方程混合初边值问题的半整体C~2解理论为基础,针对一般的二阶拟线性双曲型方程的特征根在平衡态附近的不同分布情况,分别提出了相应的一般边界条件,并采用直接构造的方法,对特征根均不为零的情况,建立了完整的局部精确边界能控性理论;对一特征根为零的情况,对一类特殊的方程建立了其精确边界能控的充分必要条件,并分别对相应的控制时间给出了估计.%Based on the theory of the semi-global C~2 solution to the mixed initial-boundary value problem for second order quasi linear hyperbolic systems, different boundary conditions are proposed for general second order quasilinear hyperbolic equations according to the distribution of the eigenvalues in a neighbourhood of the equilibrium states. The local exact boundary controllability is established by direct method for second order quasilinear hyperbolic equations with nonzero eigenvalues; for second order quasilinear hyperbolic equations with zero eigenvalues, the local exact boundary controllability is established for specific equations. Some sharp estimates on the exact controllability time are also obtained.