A Modified Kernel Method for Solving Cauchy Problem of Two-Dimensional Heat Conduction Equation

被引：7
|
作者：
Zhao, Jingjun [1 ]
Liu, Songshu [1 ]
Liu, Tao [1 ]
机构：
[1] Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China
来源：
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS | 2015年 / 7卷 / 01期
基金：
中国国家自然科学基金; 黑龙江省自然科学基金;
关键词：
Ill-posed problem; Cauchy problem; modified kernel method;
D O I：
10.4208/aamm.12-m12113
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, a Cauchy problem of two-dimensional heat conduction equation is investigated. This is a severely ill-posed problem. Based on the solution of Cauchy problem of two-dimensional heat conduction equation, we propose to solve this problem by modifying the kernel, which generates a well-posed problem. Error estimates between the exact solution and the regularized solution are given. We provide a numerical experiment to illustrate the main results.
引用
收藏
页码：31 / 42
页数：12
相关论文
共 50 条
  • [41] The asymptotics of the solution of the Cauchy problem for the two-dimensional homogeneous wave equation
    Kalyakin, LA
    Shakir'yanov, MM
    DIFFERENTIAL EQUATIONS, 1999, 35 (09) : 1307 - 1309
  • [42] The Cauchy problem associated with a two-dimensional Benjamin-Ono equation
    Preciadol, German
    BOLETIN DE MATEMATICAS, 2012, 19 (01): : 1 - 18
  • [43] Uniqueness of a solution to the cauchy problem for the hopf equation in the two-dimensional case
    Gishlarkaev V.I.
    Journal of Mathematical Sciences, 2010, 169 (1) : 64 - 83
  • [44] On the Cauchy Problem for the Wave Equation in a Two-Dimensional Domain with Data on the Boundary
    Demchenko M.N.
    Journal of Mathematical Sciences, 2023, 277 (4) : 575 - 585
  • [45] A method of fundamental solutions for two-dimensional heat conduction
    Johansson, B. Tomas
    Lesnic, Daniel
    Reeve, Thomas
    INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2011, 88 (08) : 1697 - 1713
  • [46] Multicomponent iterative method for solving two-dimensional heat transfer equation on moving grids
    Sytova, S.
    Mathematical Modelling and Analysis, 2000, 5 (01) : 164 - 174
  • [47] A polygonal element differential method for solving two-dimensional transient nonlinear heat conduction problems
    Zhou, Ling
    Lv, Jun
    Cui, Miao
    Peng, Haifeng
    Gao, Xiaowei
    ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2023, 146 : 448 - 459
  • [48] On Solving Two-Dimensional Inverse Heat Conduction Problems Using the Multiple Source Meshless Method
    Ku, Cheng-Yu
    Xiao, Jing-En
    Huang, Wei-Po
    Yeih, Weichung
    Liu, Chih-Yu
    APPLIED SCIENCES-BASEL, 2019, 9 (13):
  • [49] ON THE SOLUTION TO A TWO-DIMENSIONAL HEAT CONDUCTION PROBLEM IN A DEGENERATE DOMAIN
    Jenaliyev, M. T.
    Ramazanov, M., I
    Kosmakova, M. T.
    Tuleutaeva, Zh M.
    EURASIAN MATHEMATICAL JOURNAL, 2020, 11 (03): : 89 - 94
  • [50] Solution of a two-dimensional heat-conduction problem for a sector
    Vlasov, V.I.
    Krivoruchenko, T.N.
    Journal of Engineering Physics (English Translation of Inzhenerno-Fizicheskii Zhurnal), 1988, 54 (01): : 104 - 108
12345