【摘要】 本文将常微分方程稳定性理论中的Lyapunov第二方法应用到偏微分方程中去,着重讨论了二阶线性偏微分方程混合问题解的唯一性与稳定性;得到了三个唯一性与稳定性的定理;并通过实例说明定理的应用, 由于Lyapunov泛函比传统方法中的“能量函数”广泛得多,因而用选取适当的泛函V证明混合问题解的唯一性与稳定性要比文[1][2]中的证明简单而且广泛.更多还原

【Abstract】 In this note, uniqueness and stability of solution of the mixed problem of second-order linear partial differential equations by Lyapunov’s second method are discussed: three theorems have been obtained. The author has proved uniqueness and stability of solutions of the mixed problems of wave equations and generalized wave equations; such proofs are simpler than that by the method of energy and energy inequality’as appeared in [1],[2],[3].更多还原