Related papers: Gevrey regularity for the Euler-Bernoulli beam equ…
This paper is concerned with the study of regularity and stability properties of two Euler-Bernoulli beam equations with localized singular damping. Under suitable regularity assumptions on the damping coefficient, we establish Gevrey…
We study the Euler-Bernoulli beam model with singularities at the points $x=\xi_1$, $x=\xi_2$ and with localized viscoelastic dissipation of Kelvin-Voigt type. We assume that the beam is composed by two materials; one is an elastic material…
We consider the Euler-Bernoulli beam equation with a local Kelvin-Voigt dissipation type in the interval $(-1,1)$. The coefficient damping is only effective in $(0,1)$ and is degenerating near the $0$ point with a speed at least equal to…
In this paper, we consider the longitudinal and transversal vibrations of the transmission Euler-Bernoulli beam with Kelvin-Voigt damping distributed locally on any subinterval of the region occupied by the beam and only in one side of the…
We investigate the stability properties of an abstract class of semi-linear systems. Our main result establishes rational rates of decay for classical solutions assuming a certain non-uniform observability estimate for the linear part and…
A result of Gevrey regularity is ascertained for a semigroup which models a fluid-structure interaction problem. In this model, the fluid evolves in a piecewise smooth or convex geometry $\mathcal{O}$. On a portion of the boundary, a fourth…
This work investigates the global exponential stabilization of a degenerate Euler-Bernoulli beam subjected to a non uniform axial force and a delayed feedback control. First, we address the well-posedness of the system by constructing an…
I In this work, we present the study of the regularity of the solutions of the abstract system\eqref{Eq1.10} that includes the Euler-Bernoulli($\omega=0$) and Kirchoff-Love($\omega>0$) thermoelastic plates, we consider for both fractional…
We study, the Regularity of the Timoshenko system with two fractional dampings $(-\Delta)^\tau u_t$ and $(-\Delta)^\sigma \psi_t$; both of the parameters $(\tau, \sigma)$ vary in the interval $[0,1]$. We note that ($\tau=0$ or $\sigma=0$)…
We investigate the regularity of the strongly continuous semigroup associated with a system of two coupled second order evolution equations with indirect damping, whose stability was recently studied by Hao et al. By deriving the asymptotic…
In this work we study a strongly coupled system between the equation of plates with fractional rotational inertial force $\kappa(-\Delta)^\beta u_{tt}$ where the parameter $0 <\beta\leq 1$ and the equation of an electrical network…
We characterize all semigroups $(T(t))_{t\geq0}$ on $L^2(\Omega)$ sandwiched between Dirichlet and Neumann ones, i.e.: \begin{equation*}\label{eq:san} e^{t\Delta_D}\leq T(t)\leq e^{t\Delta_N}\quad,\text{for all }t\geq0 \end{equation*} in…
We consider the Timoshenko beam equation with locally distributed Kelvin-Voigt damping, which affects either the shear stress or the bending moment. The damping coefficient exhibits a singularity, causing its derivative to be discontinuous.…
We consider the time dependent Euler--Bernoulli beam equation with discontinuous and singular coefficients. Using an extension of the H\"ormander product of distributions with non-intersecting singular supports [L. H\"ormander, The Analysis…
In this work, we study the stability and regularity of the system formed by the third-order vibration equation in Moore-Gilson-Thompson time coupled with the classical heat equation with Fourier's law. We consider fractional couplings. He…
In this paper, we examine regularity issues for two damped abstract elastic systems; the damping and coupling involve fractional powers $\mu, \theta$, with $0 \leq \mu , \theta \leq 1$, of the principal operators. The matrix defining the…
The present work intends to complement the study of the regularity of the solutions of the thermoelastic plate with rotacional forces. The rotational forces involve the spectral fractional Laplacian, with power parameter $\tau\in [0,1]$ (…
In this paper, we examine regularity and stability issues for two damped abstract elastic systems. The damping involves the average velocity and a fractional power $\theta$, with $\theta$ in $[-1,1]$, of the principal operator. The matrix…
We consider an inhomogeneous Euler-Bernoulli (EB) beam of length $L$ clamped at both ends and subject to : an external frictional damping and a thermal effect (Fourier law). We prove the well-posedness of the model and analyze the behavior…
This paper investigates the boundary stabilization of an Euler-Bernoulli beam under constant axial tension and subject to an internal time-delay. First, the well-posedness of the system is established using semigroup of linear operators…