Related papers: The time singular limit for a fourth-order damped …
In this paper, we study asymptotic behaviors for classical thermoelastic plate equations with the Fourier law of heat conduction in the whole space $\mathbb{R}^n$, where we introduce a reduction methodology basing on third-order (in time)…
It is classical that uniform stabilization of solutions to the autonomous damped wave equation is equivalent to every geodesic meeting the positive set of the damping, which is called the geometric control condition. In this paper, it is…
This paper is concerned with the analysis of a one dimensional wave equation $z_{tt}-z_{xx}=0$ on $[0,1]$ with a Dirichlet condition at $x=0$ and a damping acting at $x=1$ which takes the form $(z_t(t,1),-z_x(t,1))\in\Sigma$ for every…
We consider a damped linear hyperbolic system modelling the propagation of pressure waves in a network of pipes. Well-posedness is established via semi-group theory and the existence of a unique steady state is proven in the absence of…
The purpose of this work is to investigate the exponential stability of a second order coupled wave equations by laplacian with one locally internal viscous damping. Firstly, using a unique continuation theorem combined with a Carleman…
The present paper deals with the parabolic-elliptic Keller-Segel equation in the plane in the general framework of weak (or ''free energy") solutions associated to initial datum with finite mass $M$, finite second moment and finite entropy.…
In this paper, we consider the asymptotic behavior of solutions to the wave equation with space-dependent damping in an exterior domain. We prove that when the damping is effective, the solution is approximated by that of the corresponding…
We establish a link between metastability and a discrete time-crystalline phase in a periodically driven open quantum system. The mechanism we highlight requires neither the system to display any microscopic symmetry nor the presence of…
In this paper, we are interested in the Cauchy problem for the viscoelastic damped wave equation with memory of type I. By applying WKB analysis and Fourier analysis, we explain the memory's influence on dissipative structures and…
In this note we analyze the large time behavior of solutions to an initial/boundary problem involving a damped nonlinear beam equation. We show that under physically realistic conditions on the nonlinear terms in the equation of motion the…
An asymptotic analysis is performed for thin anisotropic elastic plate clamped along its lateral side and also supported at a small area $\theta_{h}$ of one base with diameter of the same order as the plate thickness $h\ll1.$ A…
In this paper, we study a mixed wave-plate equation with rotational inertia, fractional damping and memory non-linearity. This research is a non-existence counterpart to a paper by D'Abbicco and Longen, in search of the critical exponent…
We investigate the time-evolution of elastoplastic materials reinforced by randomly distributed long-range interactions. Starting from a rate-independent system on a discrete spring lattice that combines local linearized elasticity,…
In this paper we study some key effects of a discontinuous forcing term in a fourth order wave equation on a bounded domain, modeling the adhesion of an elastic beam with a substrate through an elastic-breakable interaction. By using a…
In this paper we study the Hamiltonian dynamics of charged particles subject to a non-self-consistent stochastic electric field, when the plasma is in the so-called weak turbulent regime. We show that the asymptotic limit of the Vlasov…
We investigate a semilinear wave equation with energy-critical nonlinearity and a nonlinear damping mechanism driven by the total energy of the system. The model combines the quintic defocusing term with a time-dependent dissipation of the…
In this paper, we consider numerical solutions of a time domain acoustic-elastic wave interaction problem which occurs between a bounded penetrable elastic body and a compressible inviscid fluid. It is also called the fluid-solid…
For the water waves equations, the existence of splat singularities has been shown in [3], i.e., the interface self-intersects along an arc in finite time. The aim of this paper is to show the absence of splat singularities for the…
In the current work we study a stochastic parabolic problem. The underlying problem is actually motivated by the study of an idealized electrically actuated MEMS (Micro-Electro-Mechanical System) device in the case of random fluctuations of…
The singular parabolic problem $u_t-\triangle u=\lambda{\frac{1+\delta|\nabla u|^2}{(1-u)^2}}$ on a bounded domain $\Omega$ of $\mathbb{R}^n$ with Dirichlet boundary condition, models the Microelectromechanical systems (MEMS) device with…