Electron. J. Differential Equations, Vol. 2018 (2018), No. 149, pp. 1-23.

Final-value problem for a weakly-coupled system of structurally damped waves

Nguyen Huy Tuan, Vo Van Au, Nguyen Huu Can, Mokhtar Kirane

We consider the final-value problem of a system of strongly-damped wave equations. First of all, we find a solution of the system, then by an example we show the problem is ill-posed. Next, by using a filter method, we propose stable approximate (regularized) solutions. The existence, uniqueness of the corresponding regularized solutions are obtained. Furthermore, we show that the corresponding regularized solutions converge to the exact solutions in L^2 uniformly with respect to the space coordinate under some a priori assumptions on the solutions.

Submitted February 22, 2018. Published August 7, 2018.
Math Subject Classifications: 35K05, 35K99, 47J06, 47H10.
Key Words: Ill-posed problems; regularization; systems of wave equations; error estimate.

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Nguyen Huy Tuan
Applied Analysis Research Group
Faculty of Mathematics and Statistics
Ton Duc Thang University
Ho Chi Minh City, Vietnam
email: nguyenhuytuan@tdt.edu.vn
Vo Van Au
Faculty of General Sciences
Can Tho University of Technology
Can Tho City, Vietnam
email: vvau@ctuet.edu.vn
Nguyen Huu Can
Faculty of Mathematics and Computer Science
University of Science, Vietnam National University
(VNU-HCMC), Ho Chi Minh City, Vietnam
email: nguyenhuucan@gmail.com
Mokhtar Kirane
LaSIE, Faculté des Sciences, Pôle Sciences et Technologies
Université de La Rochelle
Avenue M. Crepeau, 17042 La Rochelle Cedex, France
email: mkirane@univ-lr.fr

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