Simultaneous identification of diffusion coefficient, spacewise dependent source and initial value for 1D heat equation
时 间：2018-09-28 10:00-11:00
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.