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Regularization of a two‐dimensional strongly damped wave equation with statistical discrete data
Author(s) -
Thanh Binh Tran,
Huu Can Nguyen,
Quoc Nam Danh Hua,
Ngoc Thach Tran
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6195
Subject(s) - mathematics , hadamard transform , discretization , regularization (linguistics) , inverse problem , mathematical analysis , fourier transform , wave equation , well posed problem , discrete fourier transform (general) , fourier analysis , fractional fourier transform , artificial intelligence , computer science
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.