Stability results of an elastic/viscoelastic transmission problem of locally coupled waves with non smooth coefficients

Mohammad Akil; Ibtissam Issa; Ali Wehbe

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arXiv · 2004.06758

Stability results of an elastic/viscoelastic transmission problem of locally coupled waves with non smooth coefficients

Mohammad Akil·Ibtissam Issa·Ali Wehbe

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Abstract

We investigate the stabilization of a locally coupled wave equations with only one internal viscoelastic damping of Kelvin-Voigt type. The main novelty in this paper is that both the damping and the coupling coefficients are non smooth. First, using a general criteria of Arendt-Batty, combined with an uniqueness result, we prove that our system is strongly stable. Next, using a spectrum approach, we prove the non-exponential (uniform) stability of the system. Finally, using a frequency domain approach, combined with a piecewise multiplier technique and the construction of a new multiplier satisfying some ordinary differential equations, we show that the energy of smooth solutions of the system decays polynomially of type t^{-1}.

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BibTeX RIS

Mohammad Akil, Ibtissam Issa, Ali Wehbe. 2020-04-14. Stability results of an elastic/viscoelastic transmission problem of locally coupled waves with non smooth coefficients. https://arxiv.org/abs/2004.06758

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