Well-posedness and stability for semilinear wave-type equations with time delay-Reference-Cited by-同舟云学术

Well-posedness and stability for semilinear wave-type equations with time delay

Published:2022 Issue:6 Volume:15 Page:1561
ISSN:1937-1632
Container-title:Discrete and Continuous Dynamical Systems - S
language:
Short-container-title:DCDS-S

Author:

Paolucci Alessandro¹,Pignotti Cristina¹

Affiliation:

1. Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica, Università dell'Aquila, Via Vetoio, 67010, L'Aquila, Italy

Abstract

<p style='text-indent:20px;'>In this paper, we analyze a semilinear abstract damped wave-type equation with time delay. We assume that the delay feedback coefficient is variable in time and belongs to <inline-formula><tex-math id="M1">\begin{document}$ L^1_{loc}([0, +\infty)). $\end{document}</tex-math></inline-formula> Under suitable assumptions, we show well-posedness and exponential stability for <i>small</i> initial data. Our strategy combines careful energy estimates and continuity arguments. Some examples illustrate the abstract results.</p>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis

Reference23 articles.

1. E. M. Ait Benhassi, K. Ammari, S. Boulite, L. Maniar.Feedback stabilization of a class of evolution equations with delay, J. Evol. Equ., 9 (2009), 103-121.

2. F. Alabau-Boussouira, P. Cannarsa, D. Sforza.Decay estimates for second order evolution equations with memory, J. Funct. Anal., 254 (2008), 1342-1372.

3. F. Alabau-Boussouira, S. Nicaise and C. Pignotti, Exponential stability of the wave equation with memory and time delay, in New Prospects in Direct, Inverse and Control Problems for Evolution Equations, Springer Indam Ser., (2014), 1–22.

4. K. Ammari and B. Chentouf, Asymptotic behavior of a delayed wave equation without displacement term, Z. Angew. Math. Phys., 68 (2017), Paper No. 117, 13 pp.

5. K. Ammari, S. Gerbi.Interior feedback stabilization of wave equations with dynamic boundary delay, Z. Anal. Anwend., 36 (2017), 297-327.

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