Related papers: Stability of abstract coupled systems
We use the entropy method to analyze the nonlinear dynamics and stability of a continuum kinetic model of an active nematic suspension. From the time evolution of the relative entropy -- an energy-like quantity in the kinetic model -- we…
This paper studies the asymptotic stability of solution to an initial-boundary value problem for a hyperbolic-elliptic coupled system on two-dimensional half space, where the data on the boundary and at the far field are prescribed as $u_-$…
The purpose of this work is to analyze the mathematical model governing motion of $n$-component, heat conducting reactive mixture of compressible gases. We prove sequential stability of weak variational entropy solutions when the state…
A mathematical model describing the initial stage of the capture of oscillatory systems into autoresonance under the action of slowly varying pumping is considered. Solutions with an infinitely growing amplitude are associated with the…
In this paper we consider the dynamics of harmonically-confined atomic gases. We present various general results which are independent of particle statistics, interatomic interactions and dimensionality. Of particular interest is the…
In this paper, we propose and analyze an abstract stabilized mixed finite element framework that can be applied to nonlinear incompressible elasticity problems. In the abstract stabilized framework, we prove that any mixed finite element…
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…
This paper presents finite-time and fixed-time stabilization results for inhomogeneous abstract evolution problems, extending existing theories. We prove well-posedness for strong and weak solutions, and estimate upper bounds for settling…
We study the global dynamics of the wave equation, Maxwell's equation and the linearized Bianchi equations on a fixed anti-de Sitter (AdS) background. Provided dissipative boundary conditions are imposed on the dynamical fields we prove…
In this paper we present a generalized analytical solution to the generalized state equations of coupled second-order non-autonomous circuit systems. The analytical solutions thus obtained are used to study the synchronization dynamics of…
We study a system of semilinear wave equations satisfying the weak null condition, which can be regarded as a simplified model for the Einstein vacuum equations. The main objective is to establish precise pointwise decay estimates, as both…
In this manuscript, we present the development of implicit and implicit-explicit ADER and DeC methodologies within the DeC framework using the two-operators formulation, with a focus on their stability analysis both as solvers for ordinary…
Modern distributed systems often rely on so called weakly-consistent databases, which achieve scalability by sacrificing the consistency guarantee of distributed transaction processing. Such databases have been formalised in two different…
This paper presents a generalized energy-based modeling framework extending recent formulations tailored for differential-algebraic equations. The proposed structure, inspired by the port-Hamiltonian formalism, ensures passivity, preserves…
We investigate the stability properties of discrete and hybrid stochastic nonlinear dynamical systems. More precisely, we extend the stochastic contraction theorems (which were formulated for continuous systems) to the case of discrete and…
We study cascade coupled systems, for which our prototypical example is a 1-d heat equation coupled with a 1-d wave equation. The heat component is controlled through one boundary and the information is transmitted through another one to…
The notion of stability in a structured argumentation setup characterizes situations where the acceptance status associated with a given literal will not be impacted by any future evolution of this setup. In this paper, we abstract away…
The objective of this paper is to report some computational results for the theory of DAE stability boundary, with the aim of advancing applications in power system voltage stability studies. Firstly, a new regularization transformation for…
Degenerate abstract parabolic equations with variable coefficients are studied. Here the boundary conditions are nonlocal. The maximal regularity properties of solutions for elliptic and parabolic problems and Strichartz type estimates in…
We obtain sufficient conditions for the stability of the synchronized solutions for a class of coupled dynamical systems. This is accomplished by finding an analytical expression for the transverse Liapunov exponent through spectral…