We analyze the asymptotic behavior of solutions to wave equations with strong damping terms in $\textbf{R}^n$ $(n\ge1)$, $$ u_{tt}-\Delta u-\Delta u_t=0, \qquad u(0,x)=u_0(x), \quad u_t(0,x)=u_1(x). If initial data belong suitable weighted $L^1$ spaces, lower bounds for difference between and leading Fourier space are obtained, which implies optimality expanding methods some estimates proposed ...

This paper is concerned with the multi-dimensional compressible Euler equations time-dependent damping of form $$-\frac{\mu }{(1+t)^\lambda }\rho {\varvec{u}}$$ in $${\mathbb {R}}^n$$ , where $$n\ge 2$$ $$\mu >0$$ and $$\lambda \in [0,1)$$ . When bigger, effect time-asymptotically gets weaker, which called under-damping. We show optimal decay estimates solutions such that $$\Vert \partial _x^\a...

In the current study the influence of weight percentage of HIPS, weight percentage of CNT and hardener content on damping 1st and damping 2nd properties of epoxy/HIPS/CNT hybrid composite wase valuated. Mixture design methodology was employed to generate mathematical models for predicting damping 1st and damping 2nd behaviors of new mentioned hybrid nanocomposite as function of physical factors...

We study a nonlocal wave equation with logarithmic damping, which is rather weak in the low-frequency zone as compared frequently studied strong damping case. consider Cauchy problem for this model Rn, and we asymptotic profile optimal estimates of solutions total energy t → ∞ L2 sense. In that case, some results on hypergeometric functions are useful.

in the present paper the behavior of an elastically mounted cylinder in low and high mass-damping ratio is investigated. for high mass-damping ratio, a classical wake oscillator model is used. at the first, by neglecting all damping and nonlinear terms of this model, the possibility of using a linear model for determination of the lock-in range and the dominant mode is investigated. then, witho...

In this study, a new method for the optimal design of multimode shunt-damping circuits is presented. A modification “current-flowing” shunt circuit employed to control multiple vibration modes piezoelectric laminate beam. addition resistor damping components, considers capacitances and shunting branch inductors as variables. The H? norm damped system minimized using particle swarm optimization ...

We study the stability of weakly coupled and partially damped systems by means of Riesz basis approach in higher dimension spaces. We propose a weaker distributed damping that compensates the behaviour of the eigenvalues of the system, therefore gives the optimal polynomial energy decay rate for smooth initial data.

This paper studies the properties of solutions of the Riccati equation arising from the quadratic optimal control problem of the general damped second order system. Using the semigroup theory, we establish the weak differential characterization of the Riccati equation for a general class of the second order distributed systems with arbitrary damping terms.