平板几何迁移算子的特征值问题  

Eigenvalue Problem for a Transport Equation in Slab Geometry

作　　者：王希文 王丽洁 王辉[1] 张欣[3] 任寒景 马妍 WANG Xi-wen;WANG Li-jie;WANG Hui;ZHANG Xin;REN Han-jing;MA Yan(College of Mathematical Sciences,Harbin Normal University,Harbin 150025,China;College of Science,Harbin University of Science and Technology,Harbin 150080,China;Department of Basic Courses,Beijing Union University,Beijing 100101,China;School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China;Key Laboratory of Systems and Control,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China;School of mathematical science,Mudanjiang normal university,Mudanjiang 157011,China)

机构地区：[1]哈尔滨师范大学数学科学学院,黑龙江哈尔滨150025 [2]哈尔滨理工大学理学院,黑龙江哈尔滨150080 [3]北京联合大学基础课教学部,北京100101 [4]中国科学院大学数学科学学院,北京100049 [5]中国科学院数学与系统科学研究院系统控制实验室,北京100190 [6]牡丹江师范学院数学科学学院,黑龙江牡丹江157011

出　　处：《数学的实践与认识》2020年第8期234-240,共7页Mathematics in Practice and Theory

基　　金：黑龙江省自然科学基金项目(A201305);北京市教委科研计划项目(KM201811417013);黑龙江省教育厅项目资助(1353MSYQN017);牡丹江师范学院青年项目(QN2018007)。

摘　　要：研究L^p(1<p<∞)空间平板几何各向异性散射迁移方程的特征值问题.与以往不同,利用均值投影法研究动态问题的特征值.通过运用均值投影法求特征值的近似值,从理论上证明了特征值和特征元的收敛性,并得到了更高的收敛阶数,提高了近似特征值和特征元的收敛速度.The objective of this paper is to research the problem of the eigenvalue of the anisotropic scattering transport equation in slab geometry in L^p(1<p<∞)space.Different from traditional methods,this paper utilizes the mean projection method to deal with the eigenvalue of dynamic problems.By using of the mean projection method to obtain the approximate eigenvalues,we theoretically prove the convergence of eigenvalues and eigenvectors.Furthermore,we obtained higher convergence order,and the convergence rate of approximate eigenvalues and eigenvectors is improved.

关 键 词：迁移方程 各向异性散射 均值投影 特征值 

分 类 号：O177[理学—数学]