ﻻ يوجد ملخص باللغة العربية
The paper is concerned with the exponential attractors for the viscoelastic wave model in $Omegasubset mathbb R^3$: $$u_{tt}-h_t(0)Delta u-int_0^inftypartial_sh_t(s)Delta u(t-s)mathrm ds+f(u)=h,$$ with time-dependent memory kernel $h_t(cdot)$ which is used to model aging phenomena of the material. Conti et al [Amer. J. Math., 2018] recently provided the correct mathematical setting for the model and a well-posedness result within the novel theory of dynamical systems acting on. time-dependent spaces, recently established by Conti, Pata and Temam [J. Differential Equations, 2013], and proved the existence and the regularity of the time-dependent global attractor. In this work, we further study the existence of the time-dependent exponential attractors as well as their regularity. We establish an abstract existence criterion via quasi-stability method introduced originally by Chueshov and Lasiecka [J. Dynam. Diff.Eqs.,2004], and on the basis of the theory and technique developed in [Amer. J. Math., 2018] we further provide a new method to overcome the difficulty of the lack of further regularity to show the existence of the time-dependent exponential attractor. And these techniques can be used to tackle other hyperbolic models.
This paper is concerned with system of magnetic effected piezoelectric beams with interior time-varying delay and time-dependent weights, in which the beam is clamped at the two side points subject to a single distributed state feedback controller wi
We consider the MGT equation with memory $$partial_{ttt} u + alpha partial_{tt} u - beta Delta partial_{t} u - gammaDelta u + int_{0}^{t}g(s) Delta u(t-s) ds = 0.$$ We prove an existence and uniqueness result removing the convexity assumption on the
Discretization is a fundamental step in numerical analysis for the problems described by differential equations, and the difference between the continuous model and discrete model is one of the most important problems. In this paper, we consider the
We are interested in the Moore-Gibson-Thompson(MGT) equation with memory begin{equation} onumber tau u_{ttt}+ alpha u_{tt}+c^2A u+bA u_t -int_0^tg(t-s)A w(s)ds=0. end{equation} We first classify the memory into three types. Then we study how a memory
In this paper, we first establish a criterion based on contractive function for the existence of polynomial attractors. This criterion only involves some rather weak compactness associated with the repeated limit inferior and requires no compactness,