去年在《相对论、道德经及证券研究中的“有”和“无”》一文中，我曾经科普过一个概念—适定性（well-posedness）。具体来说，一个满足适定性的问题，应该确保其：1）至少存在一个解，2）解是稳定的。
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Then it shows that the operator determined by the system is dissipative and generates a C_0 semigroup, and hence the well-posed-ness of the system follows from the semigroup theory of bounded linear operators.
然后利用有界线性算子半群的理论,证明了由闭环系统所确定的算子是预解紧的耗散算子,生成C_0压缩半群,从而得到了系统的适定性。
参考来源 - 线性Timoshenko型系统的指数镇定By means of integral equation methods creatively along with other modern mathematical theories, this paper focuses on finding solvability conditions and conditional well-posedness (especially conditional stability), constructing stabilized algorithms, and carrying through numerical simulation.
本文创造性地应用积分方程方法，借助现代数学手段，着重研究这些问题的可解性条件、条件适定性(特别是条件稳定性)，构造稳定化算法，并进行数值模拟。
参考来源 - 数学物理中反问题与边值问题的积分方程方法Since the systems (1) and (3) are equivalent, we only need study the well-poseness with a = 0 and robust stability with 0 < a < 1 of the systems (2).
利用系统(1)与(3)的等价性，通过研究系统(3)在a=0的适定性和0＜a＜1时的鲁棒稳定性，进而得出系统(1)在a=0时的适定性和0＜α＜1时的鲁棒稳定性。
参考来源 - 时滞边界反馈控制弹性梁系统的适定性和稳定性研究·2,447,543篇论文数据，部分数据来源于NoteExpress
最后给出几种特殊的人口方程的稳态解的适定性。
At last, we give the well-posed of some special population equations.
本文从最一般的人口动力系统出发，讨论其稳态解的适定性。
This paper, beginning with the general age-dependent population dynamics, discusses the well-pose of stationary solution.
本文讨论在烧蚀缓慢的情况下发汗控制微分方程并证明了其解的适定性。
In this paper, the transpiration control equation under the slow-Cremating condition is discussed and the problem is well-posed is proved.
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