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Simultaneous identification of diffusion coefficient, spacewise dependent source and initial value for 1D heat equation

2018-09-20 10:08    
主题:
Simultaneous identification of diffusion coefficient, spacewise dependent source and initial value for 1D heat equation
时间:
2018-09-28 10:00-11:00
地点:
卫津路校区第六教学楼111
主讲人:
赵志学

主讲人简介

天津师范大学博士

演讲内容介绍

    In this talk, we consider an inverse problem of determining the diffusion coefficient, spacewise dependent source term, and the initial value simultaneously for a one-dimensional heat equation based on the boundary control, boundary measurement, and temperature distribution at a given single instant in time. By a Dirichlet series representation for the boundary observation, the identification of the diffusion coefficient and initial value can be transformed into a spectral estimation problem of an exponential series with measurement error, which is solved by the matrix pencil method. For the identification of the source term, a finite difference approximation method in conjunction with the truncated singular value decomposition is adopted, where the regularization parameter is determined by the generalized cross-validation criterion. Numerical simulations are performed to verify the result of the proposed algorithm. 

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