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In this paper,under an abstract setting we establish the existence of spatially inhomogeneous steady states and the asymptotic propagation properties for a large class of monotone evolution systems without spatial translation invariance.…

Analysis of PDEs · Mathematics 2020-07-09 Taishan Yi , Xiao-Qiang Zhao

We study bounded, unbounded and blow-up solutions of a delay logistic equation without assuming the dominance of the instantaneous feedback. It is shown that there can exist an exponential (thus unbounded) solution for the nonlinear…

Dynamical Systems · Mathematics 2017-09-22 István Győri , Yukihiko Nakata , Gergely Röst

In this paper, we investigate the asymptotic behaviors of the solutions of nonlinear dynamic systems nearby an equilibrium point, when the nominal parts are subject to non necessarily small perturbations. We show that, under some estimates…

Dynamical Systems · Mathematics 2020-08-07 Mondher Benjemaa , Wided Gouadri , Mohamed Ali Hammami

We derive evolution and constraint equations for second order perturbations of flat dust homogeneous and isotropic solutions to the Einstein field equations using all scalar, vector and tensor perturbation modes. We show that the…

Mathematical Physics · Physics 2015-05-19 Filipe C. Mena

We consider the problem of constructing Lyapunov functions for linear differential equations with delays. For such systems it is known that exponential stability implies the existence of a positive Lyapunov function which is quadratic on…

Dynamical Systems · Mathematics 2007-07-03 Matthew M. Peet , Antonis Papachristodoulou , Sanjay Lall

We study the problem of stabilization for a class of evolution systems with fractional-damping. After writing the equations as an augmented system we prove in this article first that the problem is well posed. Second, using the LaSalle's…

Analysis of PDEs · Mathematics 2020-10-20 Kaïs Ammari , Fathi Hassine , Luc Robbiano

An autonomous system of ordinary differential equations describing nonlinear oscillations on the plane is considered. The influence of time-dependent perturbations decaying at infinity in time is investigated. It is assumed that the…

Dynamical Systems · Mathematics 2023-05-29 Oskar A. Sultanov

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

We consider the problem of pointwise stabilization of a one-dimensional wave equation with an internal spatially varying anti-damping term. We design a feedback law based on the backstepping method and prove exponential stability of the…

Systems and Control · Computer Science 2018-12-31 Fathi Hassine

In this work, we are concerned with a nonlinear wave equation with variable exponents. A distributive delay is imposed into the damping term with variable exponents nonlinearity. Firstly, we show that the global nonexistence time can be…

Analysis of PDEs · Mathematics 2024-11-26 Mohammad Kafini

In this paper, we discuss the asymptotic stability of singular steady states of the nonlinear heat equation in the weighted Lebesgue norms.

Analysis of PDEs · Mathematics 2009-04-27 Dominika Pilarczyk

This paper deals with an analysis and design of robust, state-feedback control law uniform-asymptotically stabilizing at origin the system consisting of coupled $n$th--order ordinary differential equations in the presence of a non-vanishing…

Optimization and Control · Mathematics 2020-12-18 Robert Vrabel

We study diffusion-type equations supported on structures that are randomly varying in time. After settling the issue of well-posedness, we focus on the asymptotic behavior of solutions: our main result gives sufficient conditions for…

Dynamical Systems · Mathematics 2020-04-28 Stefano Bonaccorsi , Francesca Cottini , Delio Mugnolo

The stability of functional differential equations under delayed feedback is investigated near a Hopf bifurcation. Necessary and sufficient conditions are derived for the stability of the equilibrium solution using averaging theory. The…

Classical Analysis and ODEs · Mathematics 2008-12-31 Fatihcan M. Atay

A two-dimensional system of differential equations with delay modelling the glucose-insulin interaction processes in the human body is considered. Sufficient conditions are derived for the unique positive equilibrium in the system to be…

Dynamical Systems · Mathematics 2020-12-11 M. Angelova , G. Beliakov , A. Ivanov , S. Shelyag

In this paper, a proof of asymptotic stability for the combined system-optimizer dynamics associated with a class of real-time methods for equality constrained nonlinear model predictive control is presented. General Q-linearly convergent…

Optimization and Control · Mathematics 2020-05-13 Andrea Zanelli , Quoc Tran-Dinh , Moritz Diehl

We analyze a classification of two main families of controllers that are of interest when the feedback loop is subject to switching propagation delays due to routing via a wireless multi-hop communication network. We show that we can cast…

Optimization and Control · Mathematics 2012-07-24 Raphael M. Jungers , Alessandro D'Innocenzo , Maria D. Di Benedetto

The topic of this paper are nonlinear traveling waves occuring in a system of damped waves equations in one space variable. We extend the freezing method from first to second order equations in time. When applied to a Cauchy problem, this…

Analysis of PDEs · Mathematics 2017-04-13 Wolf-Jürgen Beyn , Denny Otten , Jens Rottmann-Matthes

We give a proof for the asymptotic exponential stability of equilibria of quasilinear parabolic evolution equations in admissible interpolation spaces.

Analysis of PDEs · Mathematics 2018-04-30 Bogdan-Vasile Matioc , Christoph Walker

This paper proposes a unified approach for studying global exponential stability of a general class of switched systems described by time-varying nonlinear functional differential equations. Some new delay-independent criteria of global…

Dynamical Systems · Mathematics 2021-09-16 Nguyen Khoa Son , Le Van Ngoc