非自治拟线性双曲组的节点状态精确边界能控性及渐近稳定性  

Exact boundary controllability of nodal profile for nonautonomous quasilinear hyperbolic systems and its asymmetric stability

作　　者：王利彬 WANG Libin(School of Mathematical Sciences,Fudan University,200433,Shanghai,PRC)

机构地区：[1]复旦大学数学科学学院,上海市200433

出　　处：《曲阜师范大学学报（自然科学版）》2022年第3期16-22,共7页Journal of Qufu Normal University(Natural Science)

基　　金：国家自然科学基金(11831011).

摘　　要：讨论了一维非自治拟线性双曲组的节点状态精确边界能控性及其渐近稳定性,得到结论:若节点状态和已知的边界函数具有适当小的C^(1)模,则有节点状态精确边界能控性;进一步,若节点状态和已知的边界函数具有指数或多项式衰减性,则边界控制函数和相应的混合初边值问题的解也具有同样的衰减性.This paper discusses the asymptotic stability of the exact boundary controllability of nodal profile for 1-dimensional nonautonomous quasilinear hyperbolic systems.If the nodal profile and the given boundary function possess suitably small C^(1) norms,there is the exact boundary controllability of nodal profile.Furthermore,if they possess an exponential or polynomial decaying property,then the boundary control function and the solution to the corresponding mixed initial-boundary value problem possess the same decaying property.

关 键 词：非自治拟线性双曲组 经典解 节点状态精确边界能控性 渐近稳定性 

分 类 号：O175.2[理学—数学]