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This paper is devoted to the exponential stability for one-dimensional linear wave equations with in-domain localized damping and several types of Wentzell (or dynamic) boundary conditions. In a quite general boundary setting, we establish…

Analysis of PDEs · Mathematics 2025-03-31 Abdelhakim Dahmani , Yacine Chitour , Hoai-Minh Nguyen , Christophe Roman

In this paper we consider some stabilization problems for the wave equation with switching. We prove exponential stability results for appropriate damping coefficients. The proof of the main results is based on D'Alembert formula and some…

Analysis of PDEs · Mathematics 2011-11-10 Kaïs Ammari , Serge Nicaise , Cristina Pignotti

For strictly entropic Riemann shock solutions of strictly hyperbolic systems of balance laws, we prove that exponential spectral stability implies large-time asymptotic orbital stability. As a preparation, we also prove similar results for…

Analysis of PDEs · Mathematics 2022-07-27 Grégory Faye , L. Miguel Rodrigues

A mathematical model describing the initial stage of the capture of oscillatory systems into autoresonance under the action of slowly varying pumping is considered. Solutions with an infinitely growing amplitude are associated with the…

Mathematical Physics · Physics 2017-02-07 Oskar Sultanov

We study the asymptotic stability of a dissipative evolution in a Hilbert space subject to intermittent damping. We observe that, even if the intermittence satisfies a persistent excitation condition, if the Hilbert space is…

Optimization and Control · Mathematics 2012-11-26 Falk Hante , Mario Sigalotti , Marius Tucsnak

We study the exponential stability of evolutionary equations. The focus is laid on second order problems and we provide a way to rewrite them as a suitable first order evolutionary equation, for which the stability can be proved by using…

Analysis of PDEs · Mathematics 2015-05-11 Sascha Trostorff

In this paper, we obtain results on exponential stability of second order delay differential equations, which are based on a version of the Floquet theory for delay differential equations of the second order we proposed. Our version allows…

Dynamical Systems · Mathematics 2026-01-05 Alexander Domoshnitsky , Sergey Malev , Tsahi Shavit

Existence and stability of time periodic solutions for nonlinear elastic wave equations with viscoelastic terms are established. The existence of the time periodic solution is proved using the spectral decomposition of the linear principal…

Analysis of PDEs · Mathematics 2024-09-02 Yoshiyuki Kagei , Hiroshi Takeda

This paper is concerned with the asymptotic stability analysis of a one dimensional wave equation subject to a nonmonotone distributed damping. A well-posedness result is provided together with a precise characterization of the asymptotic…

Analysis of PDEs · Mathematics 2019-02-07 Swann Marx , Yacine Chitour , Christophe Prieur

Understanding how time delays impact the stability of a delay differential equation is important for modeling many natural and technological systems that experience time delays. Here we introduce a new stability criterion for…

Dynamical Systems · Mathematics 2025-08-25 Quinlan Leishman , Benjamin Webb

We consider second-order evolution equations in an abstract setting with damping and time delay and give sufficient conditions ensuring exponential stability. Our abstract framework is then applied to the wave equation, the elasticity…

Analysis of PDEs · Mathematics 2013-08-26 Serge Nicaise , Cristina Pignotti

In this paper, we address the stability of transport systems and wave propagation on networks with time-varying parameters. We do so by reformulating these systems as non-autonomous difference equations and by providing a suitable…

Analysis of PDEs · Mathematics 2016-11-07 Yacine Chitour , Guilherme Mazanti , Mario Sigalotti

A free boundary problem for the one-dimensional compressible Navier-Stokes equations is investigated. The asymptotic stability of the viscous shock wave is established under some smallness conditions. The proof is given by an elementary…

Analysis of PDEs · Mathematics 2009-12-25 Feimin Huang , Xiaoding Shi , Yi Wang

We give a proof of the exponential uniform decay of magneto-elasticity waves in a compact medium

Mathematical Physics · Physics 2012-07-04 Luiz C L Botelho

In this work, we consider the existence of global solution and the exponential decay of a nonlinear porous elastic system with time delay. The nonlinear term as well as the delay acting in the equation of the volume fraction. In order to…

Analysis of PDEs · Mathematics 2023-06-22 M. J. Dos Santos , C. A. Raposo , L. G. R. Miranda , B. Feng

In this note, we analyze an abstract evolution equation with time-dependent time delay and time-dependent delay feedback coefficient. We assume that the operator corresponding to the nondelayed part of the model generates an exponentially…

Optimization and Control · Mathematics 2024-08-07 Elisa Continelli , Cristina Pignotti

Exponential decay estimates of a general linear weakly damped wave equation are studied with decay rate lying in a range. Based on the $C^0$-conforming finite element method to discretize spatial variables keeping temporal variable…

Numerical Analysis · Mathematics 2024-06-07 P. Danumjaya , Anil Kumar , Amiya K. Pani

A condition which guaranties the exponential decay of the solutions of the initial-boundary value problem for the damped wave equation is proved. A method for the effective computability of the coefficient of exponential decay is also…

Analysis of PDEs · Mathematics 2020-09-24 Giovanni Cimatti

In this paper, we investigate the direct and indirect stability of locally coupled wave equations with local viscous damping on cylindrical and non-regular domains without any geometric control condition. If only one equation is damped, we…

Analysis of PDEs · Mathematics 2021-11-30 Mohammad Akil , Haidar Badawi , Serge Nicaise , Virginie Régnier

The time asymptotic stability for one-dimensional relaxed compressible Navier-Stokes equations is studied. We show that the composite waves of viscous shock and rarefaction are asymptotically nonlinear stable with both small wave strength…

Analysis of PDEs · Mathematics 2024-04-30 Renyong guan , Yuxi Hu