1,720,979 research outputs found
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
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)
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
Stability for some classes of degenerate nonlinear hyperbolic equations with time delay
No full textWe consider several classes of degenerate hyperbolic equations involving delay terms and suitable nonlinearities. The idea is to rewrite the problems in an abstract way and, using semigroup theory and energy method, we study well-posedness and stability. Moreover, some illustrative examples are given
Bifurcation Analysis of a Coupled System Between a Transport Equation and an Ordinary Differential Equation with Time Delay
No full textIn this paper we analyze a coupled system between a transport equation and an ordinary differential equation with time delay (which is a simplified version of a model for kidney blood flow control). Through a careful spectral analysis we characterize the region of stability, namely the set of parameters for which the system is exponentially stable. Also, we perform a bifurcation analysis and determine some properties of the stable steady state set and the limit cycle oscillation region. Some numerical examples illustrate the theoretical results
First and second-order Cucker-Smale models with non-universal interaction, time delay and communication failures
Full text linkIn this paper, we deal with first and second-order alignment models with non-universal interaction, time delay and possible lack of connection between the agents. More precisely, we analyze the situation in which the system’s agents do not transmit information to all the other agents and also agents that are linked to each other can suspend their interaction at certain times. Moreover, we take into account possible time lags in the interactions. To deal with the considered non-universal interaction, a graph topology over the structure of the model has to be considered. Under a so-called Persistence Excitation Condition, we establish the exponential convergence to consensus for both models whenever the digraph that describes the interaction between the agents is strongly connected
Time harmonic electromagnetic scattering from a bounded obstacle: an existence theorem and a computational method
No full textTime harmonic electromagnetic scattering from a bounded obstacle: an existence theorem and a computational method
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