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

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

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, uniquenes...

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Bibliographic Details
Main Authors: Nguyen Huy Tuan, Vo Van Au, Nguyen Huu Can, Mokhtar Kirane
Format: Article
Language:English
Published: Texas State University 2018-08-01
Series:Electronic Journal of Differential Equations
Subjects:
Ill-posed problems
regularization
systems of wave equations
error estimate
Online Access:http://ejde.math.txstate.edu/Volumes/2018/149/abstr.html
Description
Summary: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.
ISSN:1072-6691

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