拟线性抛物型方程可控性的定量线性近似
Quantitative linear approximation for controllability of quasi-linear parabolic equations
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中文总结 AI 辅助
本文研究拟线性抛物型方程与其线性对应方程可控性的关系，证明小初始数据下两者均零可控，控制量与状态量差异满足高阶误差估计，该方法适用于一般非线性偏微分方程且近似阶数最优。
中文摘要 AI 辅助
本文研究拟线性抛物型方程的可控性与其线性对应方程可控性之间的关系。在适当假设下，我们证明对于足够小的初始数据，两个系统均为零可控，且它们对应的控制量与状态量之间的差异满足高阶误差估计。与标准可控性问题不同，此处构造的控制量不仅能在给定终端时刻将系统导向指定目标，还能确保非线性与线性动力学之间的偏差符合上述估计。该方法适用于一般非线性偏微分方程，且可控性的近似阶数是最优的。
英文摘要
This paper studies the relationship between the controllability of a quasi-linear parabolic equation and that of its linear counterpart. Under suitable assumptions, we prove that for sufficiently small initial data both systems are null controllable, and that the differences between their corresponding controls and states satisfy a higher-order error estimate. Unlike standard controllability problems, the controls constructed here not only steer the system to a prescribed target at a given terminal time, but are also designed to ensure that the deviation between the nonlinear and linear dynamics obeys the aforementioned estimate. This method is applicable to general nonlinear partial differential equations, and the approximation order for controllability is optimal.
发表机构
- Sichuan University（四川大学）
- Northeast Normal University（东北师范大学）
机构由 AI 辅助整理，请以论文原文为准。
