Related papers: Stability of abstract coupled systems
We study stability conditions on reducible Kodaira curves obtained from degenerations of elliptic curves. We describe connected components of the spaces of stability conditions and compute the groups of deck transformations of those…
The stability of quantum systems to perturbations of the Hamiltonian is studied. This stability is quantified by the fidelity. Dependence of fidelity on the initial state as well as on the dynamical properties of the system is considered.…
In this paper, we analyze an abstract thermoelastic system, where the heat conduction follows the Cattaneo law. Zero becomes a spectrum point of the system operator when the coupling and thermal damping parameters of system satisfy specific…
This paper is concerned with the decay estimate of solutions to the semilinear wave equation subject to two localized dampings in a bounded domain. The first one is of the nonlinear Kelvin-Voigt type and is distributed around a neighborhood…
In this paper, the asymptotic behavior of abstract strongly coupled hyperbolic equations with one infinite memory term is investigated, one specific case of which is the model for describing the dynamical behaviour of magnetic effected…
The study of resonances (and well-posedness) for complex systems under time-periodic loading is of broad interest in application. The work of Galdi et al.~(2014) connects asymptotic stability of solutions to an unforced Cauchy problem to…
We develop a framework to give upper bounds on the "practical" computational complexity of stability problems for a wide range of nonlinear continuous and hybrid systems. To do so, we describe stability properties of dynamical systems using…
Abstract separation systems provide a simple general framework in which both tree-shape and high cohesion of many combinatorial structures can be expressed, and their duality proved. Applications range from tangle-type duality and tree…
The nonlinear collisional dynamics of coupled driven plasma waves in the presence of background dissipation is studied analytically within kinetic theory. Sufficiently near marginal stability, phase space correlations are poorly preserved…
The aim of this work is to show an abstract framework to analyze a family of linear degenerate parabolic mixed equations. We combine the theory for the degenerate parabolic equations with the classical Babuska-Brezzi theory for linear mixed…
In this paper, we study the impulse controllability of a multi-dimensional heat equation with dynamic boundary conditions in a bounded smooth domain. Using a recent approach based on finite-time stabilization, we show that the system is…
This paper proposes a new method, in the frequency domain, to define absorbing boundary conditions for general two-dimensional problems. The main feature of the method is that it can obtain boundary conditions from the discretized equations…
A unified approach for analyzing synchronization in coupled systems of autonomous differential equations is presented in this work. Through a careful analysis of the variational equation of the coupled system we establish a sufficient…
It has been realized in recent years that coupled focusing lattices in accelerators and storage rings have significant advantages over conventional uncoupled focusing lattices, especially for high-intensity charged particle beams. A…
We study a wave equation in one space dimension with a general diffusion coefficient which degenerates on part of the boundary. Degeneracy is measured by a real parameter $\mu_a>0$. We establish observability inequalities for weakly (when…
We study the problem of stabilization for the acoustic system with a spatially distributed damping. Imposing various hypotheses on the structural properties of the damping term, we identify either exponential or polynomial decay of…
We study a two-state quantum system with a non linearity intended to describe interactions with a complex environment, arising through a non local coupling term. We study the stability of particular solutions, obtained as constrained…
Continuum solvation methods can provide an accurate and inexpensive embedding of quantum simulations in liquid or complex dielectric environments. Notwithstanding a long history and manifold applications to isolated systems in open boundary…
Stability of a set of travelling wave solutions to the hyperbolic generalization of the convection-reaction-diffusion equation is studied by means of the qualitative methods and numerical simulation.
We study stability of solitary wave solutions for the fractional generalized Korteweg-de Vries equation $$ \partial_t u- \partial_{x_1} D^{\alpha}u+ \tfrac{1}{m}\partial_{x_1}(u^m)=0, ~ (x_1,\dots,x_d)\in \mathbb{R}^d, \, \, t\in…