Related papers: Block operator matrix techniques for stability pro…
In this paper we study the stability properties of strongly continuous semigroups generated by block operator matrices. We consider triangular and full operator matrices whose diagonal operator blocks generate polynomially stable…
Considering a two-by-two block operator matrix system of Maxwell type, we present an elementary way of deducing exponential stability under minimal smoothness (and boundedness) requirements of the underlying domains when applications are…
New approaches to the study of stability of solutions of Set Differential Equations (SDEs) based on convex geometry and the theory of mixed volumes were proposed. The stability of the forms of program solutions of linear SDEs with a stable…
In the present work, we demonstrate how the pseudoinverse concept from linear algebra can be used to represent and analyze the boundary conditions of linear systems of partial differential equations. This approach has theoretical and…
We study mild solutions of a class of stochastic partial differential equations, involving operators with polynomially bounded coefficients. We consider semilinear equations under suitable hyperbolicity hypotheses on the linear part. We…
Any numerical method fails to provide us with acceptable results if not equipped with appropriate boundary conditions. Catering to more realistic applications, in the present article we have extended the work done on the one plus one…
In this paper we analyze the stability of equilibrium manifolds of hyperbolic shallow water moment equations. Shallow water moment equations describe shallow flows for complex velocity profiles which vary in vertical direction and the…
We analyze the stability of Maxwell equations in bounded domains taking into account electric and magnetization effects. Well-posedness of the model is obtained by means of semigroup theory. A passitivity assumption guarantees the…
We consider a damped linear hyperbolic system modelling the propagation of pressure waves in a network of pipes. Well-posedness is established via semi-group theory and the existence of a unique steady state is proven in the absence of…
This paper gives necessary and sufficient conditions for the convergence of the solution of a weakly damped second order linear differential equation that is subjected to outside forcing, for which solutions of the unforced equation are…
We extend the Kreiss--Majda theory of stability of hyperbolic initial--boundary-value and shock problems to a class of systems, notably including the equations of magnetohydrodynamics (MHD), for which Majda's block structure condition does…
We design observer-based controllers to stabilise abstract linear boundary control systems on Hilbert spaces. Our main results introduce conditions for exponential, strong, and polynomial stability, and establish external well-posedness of…
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…
Motivated by the study of conditional stability of traveling waves, we give an elementary $H^2$ center stable manifold construction for quasilinear parabolic PDE, sidestepping apparently delicate regularity issues by the combination of a…
We study, for times of order 1/h, solutions of Maxwell's equations in an O(h^2) modulation of an h-periodic medium. The solutions are of slowly varying amplitude type built on Bloch plane waves with wavelength of order h. We construct…
The aim of this article is to investigate the well-posedness, stability and convergence of solutions to the time-dependent Maxwell's equations for electric field in conductive media in continuous and discrete settings. The situation we…
This paper is concerned with the asymptotic stability analysis of a one dimensional wave equation subject to a nonmonotone distributed damping. A well-posedness result is provided together with a precise characterization of the asymptotic…
Maxwell's equations are considered with transparent boundary conditions, for initial conditions and inhomogeneity having support in a bounded, not necessarily convex three-dimensional domain or in a collection of such domains. The numerical…
We investigate the stability properties of strongly continuous semigroups generated by operators of the form $A-BB^\ast$, where $A$ is a generator of a contraction semigroup and $B$ is a possibly unbounded operator. Such systems arise…
The stability of stationary solutions of first-order systems of PDE's are considered. They may include some singular geometric terms, leading to discontinuous flux and non-conservative products. Based on several examples in Fluid Mechanics,…