An extension of a Lyapunov approach to the stabilization of second order coupled systems
ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 19.

This paper deals with the convergence to zero of the energy of the solutions of a second order linear coupled system. It revisits some previous results on the stabilization of such systems by exhibiting Lyapunov functions. The ones used are constructed according to some scalar cases situations. These simpler situations explicitely show that the assumptions made on the operators in the coupled systems seem, first, natural and, second, give insight on their forms.

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DOI : 10.1051/cocv/2019075
Classification : 35B40, 49J15, 49J20
Mots-clés : damping, linear evolution equations, dissipative hyperbolic equation, decay rates, Lyapunov function 
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     author = {Horsin, Thierry and Jendoubi, Mohamed Ali},
     title = {An extension of a {Lyapunov} approach to the stabilization of second order coupled systems},
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     publisher = {EDP-Sciences},
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Horsin, Thierry; Jendoubi, Mohamed Ali. An extension of a Lyapunov approach to the stabilization of second order coupled systems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 19. doi : 10.1051/cocv/2019075. http://www.numdam.org/articles/10.1051/cocv/2019075/

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Cité par Sources :

The first author wishes to thank the Tunisian Mathematical Society (SMT) for its kind invitation to its annual congress during which this work was completed.

The second author wishes to thank the department of mathematics and statistics EPN6 and the research department M2N (EA7340) of the CNAM where this work was initiated.

Both authors are grateful to the reviewers for their helpful comments and suggestions.