含时变源的弥散黏滞波方程的重构  

RECONSTRUCTION OF THE DIFFUSIVE VISCOUS WAVE EQUATION WITH TIME-VARYING SOURCES

作　　者：林燕鸿 王然[1,2,3] 张冉 康彤 Lin Yanhong;Wang Ran;Zhang Ran;Kang Tong(Communication University of China,School of Data Science and Intelligent Media,Beijing 100024,China;Key Laboratory of Earth System Numerical Modeling and Application,University of Chinese Academy of Sciences,Beijing 100049,China;Key Laboratory of Computational Geodynamics,University of Chinese Academy of Sciences,Beijing 100049,China)

机构地区：[1]中国传媒大学,数据科学与智能媒体学院,北京100024 [2]中国科学院大学,地球系统数值模拟与应用全国重点实验室,北京100049 [3]中国科学院大学,计算地球动力学重点实验室,北京100049

出　　处：《计算数学》2024年第4期449-468,共20页Mathematica Numerica Sinica

基　　金：国家自然科学基金(42074108,U2039207);国家重点研发计划(2020YFA 0713401);中央高校基本科研业务费专项资金资助.

摘　　要：本文的目的是重构含时变源的弥散黏滞波方程.源可以分为未知的时间部分和已知的空间部分,未知部分借助非全域范围的额外探测值确定.我们提出了一种基于额外探测值的源重构方法,并证明了弱解的存在唯一性.最后通过算例对理论结果进行了验证.he purpose of this paper is to reconstruct the diffusive viscous wave equation with timevarying sources.The source can be divided into an unknown temporal part and a known spatial part.The unknown part is determined by additional detection values within a nonglobal scope.We propose a source reconstruction method based on the additional detection values and prove the existence and uniqueness of the weak solution.Finally,the theoretical results are verified through numerical examples.

关 键 词：弥散黏滞波方程 源重构 时间离散 存在唯一性 

分 类 号：O175[理学—数学]