一类指标2延迟积分代数方程的正则性研究  

Regularity analysis for a class of index-2integral-algebraic equations with a delay

作　　者：王妍婷 闫晗 梁慧[1] WANG Yanting;YAN Han;LIANG Hui(School of Mathematical Science,Heilongjiang University,Harbin 150080,China)

机构地区：[1]黑龙江大学数学科学学院,哈尔滨150080

出　　处：《黑龙江大学自然科学学报》2020年第3期290-307,共18页Journal of Natural Science of Heilongjiang University

基　　金：Supported by the National Natural Science Foundation of China (11771128);the Youth Science Foundation of Heilongjiang University (QL201201)。

摘　　要：积分代数方程是第一类和第二类Volterra积分方程的混合系统,具有十分广泛的应用,如热传导和黏弹性中的记忆核识别问题、小密室中的化学反应问题、Kirchhoff定律等。主要针对一类半显形式指标2的延迟积分代数方程,研究延迟对方程解的正则性的影响。借助于解析解的预解表达式及数学归纳法,根据延迟逐区间地证明了解析解的存在唯一性,继而对正则性进行了详细的描述。‘Mixed’ systems of integral-algebraic equations consisting of second-kind and first-kind Volterra integral equations(VIEs) have rich applications, such as memory kernel identification problems in heat conduction and viscoelasticity, evolution of a chemical reaction within a small cell, and Kirchhoff’s laws, etc. For a class of semi-explicit index-2 integral-algebraic equations with a delay, how the delay influences the regularity of the integral-algebraic equation is investigated. In view of the mathematical induction method and the resolvent representation of the analytic solution, the existence and uniqueness of the analytic solution are proved interval by interval according to the delay, and the regularity is described in detail.

关 键 词：指标2积分代数方程 常延迟 存在性 唯一性 正则性 

分 类 号：O241.83[理学—计算数学]