Related papers: Exponential stability of solutions to perturbed su…
In this paper we study the global exponential stability in the $L^{2}$ norm of semilinear $1$-$d$ hyperbolic systems on a bounded domain, when the source term and the nonlinear boundary conditions are Lipschitz. We exhibit two sufficient…
In this paper we are concerned with a initial boundary-value problem for a coupled system of two KdV equations, posed on the positive half line, under the effect of a localized damping term. The model arises when modeling the propagation of…
We improve the preceding results obtained by the first and the second authors in [3]. They concern the stability issue of the inverse problem that consists in determining the potential and the damping coefficient in a wave equation from an…
We consider the stationary Quasi-Geostrophic equation in the whole space $\mathbb R^2$ driven by a force $f$. Under certain smallness assumptions of $f$, we establish the existence of solutions with finite $L^2$ norm. This solution is…
We consider a class of abstract quasilinear parabolic problems with lower--order terms exhibiting a prescribed singular structure. We prove well--posedness and Lipschitz continuity of associated semiflows. Moreover, we investigate global…
In this paper, we embark on a captivating exploration of the stabilization of locally transmitted problems within the realm of two interconnected wave systems. To begin, we wield the formidable Arendt-Batty criteria\cite{AW} to affirm the…
We study the long-time behaviour of helically symmetric infinite-energy solutions to the incompressible Navier-Stokes equations in the whole space $\mathbb{R}^3$. Our solutions are $H^1$-perturbations of a Lamb-Oseen vortex whose…
We prove the existence and the linear stability of small amplitude time {\it quasi-periodic} standing wave solutions (i.e. periodic and even in the space variable $ x $) of a $ 2 $-dimensional ocean with infinite depth under the action of…
This article is concerned with the energy decay of an infinite memory wave equation with a logarithmic nonlinear term and a frictional damping term. The problem is formulated in a bounded domain in $\mathbb R^d$ ($d\ge3$) with a smooth…
An asymptotic stability result for parabolic semilinear problems in $L_2(\Omega)$ and interpolation spaces is shown. Some known results about stability in $W^{1,2}(\Omega)$ are improved for semilinear parabolic mixed boundary value…
In this paper, we investigate the stabilization of a locally coupled wave equations with local viscoelastic damping of past history type acting only in one equation via non smooth coefficients. First, using a general criteria of…
In this paper we establish a complete local theory for the energy-critical nonlinear wave equation (NLW) in high dimensions ${\mathbb R} \times {\mathbb R}^d$ with $d \geq 6$. We prove the stability of solutions under the weak condition…
We study pointwise convergence of the solution to the elastic wave equation to the initial data which lies in the Sobolev spaces. We prove that the solution converges along every lines to the initial data almost everywhere whenever the…
In convex planar domains, given an initial vorticity with one sign, we study the regularity and geometric properties of the dynamically stable solutions to the Euler equations in the coadjoint orbit of the initial vorticity. These flows…
This paper contains the second part of a two-part series on the stability and instability of extreme Reissner-Nordstrom spacetimes for linear scalar perturbations. We continue our study of solutions to the linear wave equation on a suitable…
We establish the full asymptotic stability of solitary waves for the focusing cubic Schr\"odinger equation on the line under small even perturbations in weighted Sobolev norms. The strategy of our proof combines a space-time resonances…
We consider the stability problem for standing waves of nonlinear Dirac models. Under a suitable definition of linear stability, and under some restriction on the spectrum, we prove at the same time orbital and asymptotic stability. We are…
For vibrating systems, a delay in the application of a feedback control can destroy the stabilizing effect of the control. In this paper we consider a vibrating string that is fixed at one end and stabilized with a boundary feedback with…
In this paper, we study transverse linear stability of line solitary waves to the $2$-dimensional Benney-Luke equation which arises in the study of small amplitude long water waves in $3$D. In the case where the surface tension is weak or…
We consider the spatially inhomogeneous Landau equation with initial data that is bounded by a Gaussian in the velocity variable. In the case of moderately soft potentials, we show that weak solutions immediately become smooth and remain…