相关论文: Polynomial Stability of Non-Linearly Damped Contra…

We prove structural stability under perturbations for a class of discrete-time dynamical systems near a non-hyperbolic fixed point. We reformulate the stability problem in terms of the well-posedness of an infinite-dimensional nonlinear…

We construct steady states of the Euler-Poisson system with a barotropic equation of state as minimizers of a suitably defined energy functional. Their minimizing property implies the non-linear stability of such states against general,…

We give a necessary and sufficient condition, of geometric type, for the uniform decay of energy of solutions of the linear system of magnetoelasticity in a bounded domain with smooth boundary. A Dirichlet-type boundary condition is…

This note is devoted to the linear stability of the Couette flow for the non-isentropic compressible Euler equations in a domain $\mathbb{T}\times \mathbb{R}$. Exploiting the several conservation laws originated from the special structure…

We study the steady uniphase and multiphase solutions of the discretized nonlinear damped wave equation.Conditions for the stability abd instability of the steady solutions are given;in the instability case the linear stable and unstable…

In this paper we investigate regularity properties of weak solutions to a PDE system that arises in the study of biological transport networks. The system consists of a possibly singular elliptic equation for the scalar pressure of the…

We show uniqueness and stability in $L^2$ and for all time for piecewise-smooth solutions to hyperbolic balance laws. We have in mind applications to gas dynamics, the isentropic Euler system and the full Euler system for a polytropic gas…

This paper establishes limit theorems and quantitative statistical stability for a class of piecewise partially hyperbolic maps that are not necessarily continuous nor locally invertible. By employing a flexible functional-analytic…

We study the behaviour of circular flexible loops sedimenting in a viscous fluid by numerical simulations and linear stability analysis. The numerical model involves a local slender-body theory approximation for the flow coupled to the…

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…

This paper focuses on establishing the existence of a class of steady solutions, termed least total curvature solutions, to the incompressible Euler system in a strip. The solutions obtained in this paper complement the least total…

We study a Euler-Bernoulli beam equation with localized discontinuous structural damping. As our main result, we prove that the associated $C_0$-semigroup $(S(t))_{t\geq0}$ is of Gevrey class $\delta>24$ for $t>0$, hence immediately…

This paper investigates the robustness of exponential stability of a class of switched systems described by linear functional differential equations under arbitrary switching. We will measure the stability robustness of such a system,…

Bead spring models for polymers in solution are nonlinear if either the finite extensibility of the polymer, excluded volume effects or hydrodynamic interactions between polymer segments are taken into account. For such models we use a…

A theory for stabilization of quantum resonances by a mechanism similar to one leading to classical resonances in nonlinear systems is presented. It explains recent surprising experimental results, obtained for cold Cesium atoms when driven…

This paper derives two stabilizability theorems for a basic class of discrete-time nonlinear systems with multiple unknown parameters. First, we claim that a discrete-time multi-parameter system is stabilizable if its nonlinear growth rate…

We carry out a comprehensive linear stability analysis of active Brownian particle systems around a constant homogeneous state. These scalar models, being important prototypes for the continuous description of active matter, are…

We consider a transmission problem where a structurally damped plate equation is coupled with a damped or undamped wave equation by transmission conditions. We show that exponential stability holds in the damped-damped situation and…

Extending results of Oh--Zumbrun and Johnson--Zumbrun for parabolic conservation laws, we show that spectral stability implies nonlinear stability for spatially periodic viscous roll wave solutions of the one-dimensional St. Venant…

We consider the incompressible Euler equations in the half cylinder $ \mathbb{R}_{>0}\times\mathbb{T}$. In this domain, any vorticity which is independent of $x_2$ defines a stationary solution. We prove that such a stationary solution is…