JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (6): 74-80.doi: 10.6040/j.issn.1671-9352.0.2020.539

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Quasi-boundary value regularization method for inhomogeneous sideways heat equation

WANG Feng-xia, XIONG Xiang-tuan*   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2021-06-03

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Abstract: In the inhomogeneous sideways heat equation, it is assumed that the heat source is largely dependent on space and time and cannot be ignored. Since the solution of the problem(if it exists)is discontinuously dependent on the data, this is a typical ill-posed problem, and most of the literature only deals with homogeneous sideways heat equation. By using Fourier transform and quasi-boundary value regularization method, the inhomogeneous sideways heat equation is studied, and the stable approximate solution is obtained. The error estimate of the stability is given under the prior parameter selection and the posterior parameter selection rule.

Key words: inhomogeneous sideways heat equation, ill-posed problems, quasi-boundary value method, error estimation

CLC Number: 

  • O241.1
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