299 research outputs found
Exponential decay for semilinear wave equations with viscoelastic damping and delay feedback
No full textIn this paper we study a class of semilinear wave-type equations with viscoelastic damping and delay feedback with time variable coefficient. By combining semigroup arguments, careful energy estimates and an iterative approach we are able to prove, under suitable assumptions, a well-posedness result and an exponential decay estimate for solutions corresponding to small initial data. This extends and concludes the analysis initiated in Nicaise and Pignotti (J Evol Equ 15:107–129, 2015) and then developed in Komornik and Pignotti (Math Nachr, to appear, 2018), Nicaise and Pignotti (Evol Equ 18:947–971, 2018)
Asymptotic Analysis of a Cucker–Smale System with Leadership and Distributed Delay
No full textWe extend the analysis developed in Pignotti and Reche Vallejo (J Math Anal Appl 464:1313–1332, 2018) [34] in order to prove convergence to consensus results for a Cucker–Smale type model with hierarchical leadership and distributed delay. Flocking estimates are obtained for a general interaction potential with divergent tail. We analyze also the model when the ultimate leader can change its velocity. In this case we give a flocking result under suitable conditions on the leader’s acceleration
material of Cocos nucifera var. palmyrensis (Beccari) Pignotti & Baldini. A. Lectotype; B. Syntype. [A: FI018792; B: FI018793] [Photos: D. Nesti, L. Pignotti] in Unraveling the taxonomic identity of Cocos nucifera f. palmyrensis (Arecaceae: Cocoseae)
No full textmaterial of Cocos nucifera var. palmyrensis (Beccari) Pignotti & Baldini. A. Lectotype; B. Syntype. [A: FI018792; B: FI018793] [Photos: D. Nesti, L. Pignotti]Published as part of Harries, Hugh C., Pignotti, Lia & Baldini, Riccardo M., 2020, Unraveling the taxonomic identity of Cocos nucifera f. palmyrensis (Arecaceae: Cocoseae), pp. 25-30 in Candollea 75 (1) on page 28, DOI: 10.15553/c2020v751a2, http://zenodo.org/record/568458
A Note on the Asymptotic Stability of Wave-Type Equations with Switching Time-Delay
No full textInternational audienceWe consider second-order evolution equations with intermittently delayed/not-delayed damping. We give sufficient conditions for asymptotic and exponential stability, completing our previous results from Nicaise and Pignotti [Adv. Diff. Eq., 17: 879–902, 2012; J. Dyn. Diff. Eq., 26: 781–803, 2014]. Moreover, some concrete models are described
Well-posedness and exponential decay estimates for a Korteweg–de Vries–Burgers equation with time-delay
No full textWe consider the KdV–Burgers equation and its linear version in presence of a delay feedback. We prove well-posedness of the models and exponential decay estimates under appropriate conditions on the damping coefficients. Our arguments rely on a Lyapunov functional approach combined with a step by step procedure and semigroup theory
Convergence to consensus of the general finite-dimensional Cucker-Smale model with time-varying delays
No full textWe consider the well known finite-dimensional Cucker-Smale system, modelling interacting collective dynamics and their possible convergence to consensus. The objective of this paper is to study the influence of time delays in the general model on the convergence to consensus. By a Lyapunov functional approach, we establish convergence results to consensus for symmetric and nonsymmetric communication weights under some structural conditions
A relaxation result for a class of degenerate Hamilton-Jacobi equations
No full textIn this paper we prove a relaxation result for a class of degenerate
Hamilton–Jacobi equations; i.e., equations which do not admit
a strict subsolution, extending in some directions the results in [6] and
[7]
EXPONENTIAL SYNCHRONIZATION OF KURAMOTO OSCILLATORS WITH TIME DELAYED COUPLING
No full textWe discuss the asymptotic frequency synchronization for the non-identical Kuramoto oscillators with time delayed interactions. We provide explicit lower bound on the coupling strength and upper bound on the time delay in terms of initial configurations ensuring exponential synchronization. This generalizes not only the frequency synchronization estimate by Choi et al. [Phys. D, 241(7):735{754, 2012] for the non-identical Kuramoto oscillators without time delays but also improves previous result by Schmidt et al. [Automatica, 48(12):3008{3017, 2012] in the case of homogeneous time delays where the initial phase diameter is assumed to be less than pi/2. The proof relies on a Lyapunov functional approach
Flocking estimates for the Cucker–Smale model with time lag and hierarchical leadership
No full textWe analyze the Cucker-Smale model under hierarchical leadership in presence of a time delay. By using a Lyapunov functional approach and some induction arguments we will prove convergence to consensus for every positive delay τ. We also prove a flocking estimate in the case of a free-will leader. These results seem to point out the advantage of a hierarchical structure in order to contrast time delay effects that frequently appear in real situations
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