某些具有常系数的一维线性双曲平衡律的最小零控时间及相关核方程的性质
Minimal null control time of some 1D linear hyperbolic balance laws with constant coefficients and properties of related kernel equations
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中文总结 AI 辅助
本文研究一维常系数双曲平衡律的零能控性，通过核方程分析，给出最小零控时间与正交性条件的关系及显式界，并推广至有限时间镇定。
中文摘要 AI 辅助
本文研究了一维常系数双曲平衡律在单侧边界控制下的零能控性。我们的第一个结果表明，当系统仅具有一个负速度或正速度时，此类系统的最小零控时间取决于特定序列的正交性条件。该序列由系统系数显式给出，但通过非线性递推关系定义。我们的第二个结果则通过给出在两种非平凡情形下需检验的正交性条件数量的显式界，完善了前一个结果。证明依赖于对系统相关所谓核方程的细致分析，包括一个新的适定性结果。我们的结果同样适用于有限时间镇定性质。
英文摘要
In this work, we study the null controllability by one-sided boundary controls of one-dimensional hyperbolic balance laws with constant coefficients. Our first result shows that, when the system has only one negative or positive speed, the minimal null control time of such systems depends on some orthogonality conditions for a particular sequence. This sequence is explicit in function of the coefficients of the system but it is defined by a nonlinear recurrence relation. Our second result then completes the previous one by giving explicit bounds on the number of orthogonality conditions that have to be checked in two nontrivial situations. The proofs rely on a careful analysis of the so-called kernel equations associated with the system, including a new well-posedness result. Our results are also valid for the finite-time stabilization property.
发表机构
- School of Mathematics, Shandong University（山东大学数学学院）
- Faculty of Mathematics and Computer Science, Jagiellonian University（雅盖隆大学数学与计算机科学学院）
机构由 AI 辅助整理，请以论文原文为准。
