Regularization of a two‐dimensional strongly damped wave equation with statistical discrete data

In this paper, we consider an inverse problem for a strongly damped wave equation in two dimensional with statistical discrete data. Firstly, we give a representation for the solution and then present a discretization form of the Fourier coefficients. Secondly, we show that the solution does not dep...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2020-05, Vol.43 (7), p.4317-4335, Article mma.6195
Main Authors: Thanh Binh, Tran, Huu Can, Nguyen, Quoc Nam, Danh Hua, Ngoc Thach, Tran
Format: Article
Language:English
Subjects:
error estimate
Inverse problems
Least squares method
Regularization
strongly damped wave
Wave equations
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Summary:In this paper, we consider an inverse problem for a strongly damped wave equation in two dimensional with statistical discrete data. Firstly, we give a representation for the solution and then present a discretization form of the Fourier coefficients. Secondly, we show that the solution does not depend continuously on the data by stating a concrete example, which makes the solution be not stable and thus the present problem is ill‐posed in the sense of Hadamard. Next, we use the trigonometric least squares method associated with the Fourier truncation method to regularize the instable solution of the problem. Finally, the convergence rate of the error between the regularized solution and the sought solution is estimated and also investigated numerically.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.6195