Related papers: Gevrey regularity for the Euler-Bernoulli beam equ…

We deal with a class of semilinear nonlocal differential equations in Hilbert spaces which is a general model for some anomalous diffusion equations. By using the theory of integral equations with completely positive kernel together with…

This note is focused on a novel technique in order to establish the boundedness in more regular spaces for global attractors of dissipative dynamical systems, without appealing to uniform-in-time estimates. As an application of the abstract…

In this article, we examine the well-posedness and asymptotic behavior of the energy associated with the wave equation that incorporates a Kelvin-Voigt nonlocal damping structure given by $-||\nabla u_t(t)||_2^2 \Delta u_t$. Utilizing the…

Main purpose of this paper is to study the following semi-linear structurally damped wave equation with nonlinearity of derivative type: $$u_{tt}- \Delta u+ \mu(-\Delta)^{\sigma/2} u_t= |u_t|^p,\quad u(0,x)= u_0(x),\quad u_t(0,x)=u_1(x),$$…

We consider the 2-D incompressible Euler equations in a bounded domain and show that local weak solutions are exponentially integrable, uniformly in time, under minimal integrability conditions. This is a Serrin-type interior regularity…

A key characteristic of the anomalous sub-solution equation is that the solution exhibits algebraic decay rate over long time intervals, which is often refered to the Mittag-Leffler type stability. For a class of power nonlinear…

Associated to every group with a weak spherical Tits system of rank n+1 with an appropriate rank n subgroup, we construct a relative spectral sequence involving group homology of Levi subgroups of both groups. Using the fact that such Levi…

In this work, we study continuity and topological structural stability of attractors for nonautonomous random differential equations obtained by small bounded random perturbations of autonomous semilinear problems. First, we study existence…

A stable $\infty$-category is $1$-semiadditive if the norms for all finite group actions are equivalences. In the presence of $1$-semiadditivity, Goodwillie calculus simplifies drastically. We introduce two variants of $1$-semiadditivity…

The exponential decay rate of the semigroup $S(t)=e^{t\mathbb{A}}$ generated by the abstract damped wave equation $$\ddot u + 2f(A) \dot u +A u=0 $$ is here addressed, where $A$ is a strictly positive operator. The continuous function $f$,…

We study the Siegel--Schr\"oder center problem on the linearization of analytic germs of diffeomorphisms in several complex variables, in the Gevrey--$s$, $s>0$ category. We introduce a new arithmetical condition of Bruno type on the linear…

We consider $N$ Euler-Bernoulli beams and $N$ strings alternatively connected to one another and forming a particular network which is a chain beginning with a string. We study two stabilization problems on the same network and the spectrum…

We consider an abstract system of Timoshenko type $$ \begin{cases} \rho_1{{\ddot \varphi}} + a A^{\frac12}(A^{\frac12}\varphi + \psi) =0\\ \rho_2{{\ddot \psi}} + b A \psi + a (A^{\frac12}\varphi + \psi) - \delta A^\gamma {\theta} = 0\\…

This paper investigates the stability of a class of differential systems time-changed by $E_{t}$ which is the inverse of a $\beta$-stable subordinator. In order to explore stability, a time-changed Gronwall's inequality and a generalized…

For a domain $\Omega \subset \mathbb{R}^n$ and a small number $\frak{T} > 0$, let \[ \mathcal{E}_0(\Omega) = \lambda_1(\Omega) + {\frak{T}} {\text{tor}}(\Omega) = \inf_{u, w \in H^1_0(\Omega)\setminus \{0\}} \frac{\int |\nabla u|^2}{\int…

In this paper, we consider the stabilization of the generalized Rao-Nakra beam equation, which consists of four wave equations for the longitudinal displacements and the shear angle of the top and bottom layers and one Euler-Bernoulli beam…

Let A be a positive self-adjoint linear operator acting on a real Hilbert space H and $\alpha$, c be positive constants. We show that all solutions of the evolution equation u + Au + cA $\alpha$ u = 0 with u(0) $\in$ D(A 1 2), u (0) $\in$ H…

We derive novel guaranteed lower bounds for eigenvalues of the Euler-Bernoulli beam with variable bending stiffness. While the standard finite element Rayleigh-Ritz method automatically yields upper bounds, we obtain lower bounds by…

We are concerned with the inverse problem of determining both the potential and the damping coefficient in a dissipative wave equation from boundary measurements. We establish stability estimates of logarithmic type when the measurements…

In this paper, we prove that a sequence of generalized eigenvectors of a linear unbounded operator associated with an Euler-Bernoulli beam equation under bending moment boundary feedback forms a Riesz basis for the underlying state Hilbert…