相关论文: Stability for multiple Lamb dipoles
We revisit the classical problem of absolute stability; assessing the robust stability of a given linear time-invariant (LTI) plant in feedback with a nonlinearity belonging to some given function class. Standard results typically take the…
Answering a question left open in \cite{MZ2}, we show for general symmetric hyperbolic boundary problems with constant coefficients, including in particular systems with characteristics of variable multiplicity, that the uniform Lopatinski…
The instabilities observed in direct numerical simulations of the Gross-Neveu equation under linear and harmonic potentials are studied. The Lakoba algorithm, based on the method of characteristics, is performed to numerically obtain the…
Frequency responses of multi-degree-of-freedom mechanical systems with weak forcing and damping can be studied as perturbations from their conservative limit. Specifically, recent results show how bifurcations near resonances can be…
This article presents a modeling framework for a class of multiphase chemical systems based on non-equilibrium thermodynamics. Compartmental modeling is used to establish the dynamic properties of liquid-vapor systems operating far from…
This paper studies finite-time stability and instability theorems in probability sense for stochastic nonlinear systems. Firstly, a new sufficient condition is proposed to guarantee that the considered system has a global solution.…
In 2002, Fatiha Alabau, Piermarco Cannarsa and Vilmos Komornik investigated the extent of asymptotic stability of the null solution for weakly coupled partially damped equations of the second order in time. The main point is that the…
Fixed-time stable dynamical systems are capable of achieving exact convergence to an equilibrium point within a fixed time that is independent of the initial conditions of the system. This property makes them highly appealing for designing…
We simulate by lattice Boltzmann the steady shearing of a binary fluid mixture undergoing phase separation with full hydrodynamics in two dimensions. Contrary to some theoretical scenarios, a dynamical steady state is attained with finite…
We address the classic problem of stability and asymptotic stability in the sense of Lyapunov of the equilibrium point of autonomic differential equations using discrete approach. This new approach includes a consideration of a family of…
We study the non relativistic motions of a charged particle in the electromagnetic field generated by two parallel electrically neutral vertical wires carrying time depends currents. Under quantitative conditions on the currents we prove…
The linear stability of two exact stationary solutions of the parametrically driven, damped nonlinear Dirac equation is investigated. Stability is ascertained through the resolution of the eigenvalue problem, which stems from the…
Stability is a key property of both forward models and inverse problems, and depends on the norms considered in the relevant function spaces. For instance, stability estimates for hyperbolic partial differential equations are often based on…
A mathematical proof for the stability of mKdV breathers is announced. This proof involves the existence of a nonlinear equation satisfied by all breather profiles, and a new Lyapunov functional which controls the dynamics of small…
In this paper, we review recent results on stability and instability in logarithmic Sobolev inequalities, with a particular emphasis on strong norms. We consider several versions of these inequalities on the Euclidean space, for the…
This paper surveys various results concerning stability for the dynamics of Lagrangian (or Hamiltonian) systems on compact manifolds. The main, positive results state, roughly, that if the configuration manifold carries a hyperbolic metric,…
The main goal of this paper is to explore the leapfrogging phenomenon in the inviscid planar flows. We show for 2d Euler equations that under suitable constraints, four concentrated vortex patches leapfrog for all time. When observed from a…
We analyze the exponential stability of distributed parameter systems. The system we consider is described by a coupled parabolic partial differential equation with spatially varying coefficients. We approximate the coefficients by…
We present two results related to magnetized Vlasov equations. Our first contribution concerns the stability of solutions to the magnetized Vlasov-Poisson system with a non-uniform magnetic field using the optimal transport approach…
Within the framework of Lagrangian mechanics, the conservativeness of the hydrostatic forces acting on a floating rigid body is proved. The representation of the associated hydrostatic potential is explicitly worked out. The invariance of…