Related papers: On the output stabilizability of the diffusion equ…
A small-gain approach is proposed to analyze closed-loop stability of linear diffusion-reaction systems under finite-dimensional observer-based state feedback control. For this, the decomposition of the infinite-dimensional system into a…
The conditioning of the linear finite volume element discretization for general diffusion equations is studied on arbitrary simplicial meshes. The condition number is defined as the ratio of the maximal singular value of the stiffness…
We study a numerical method for convection diffusion equations, in the regime of small viscosity. It can be described as an exponentially fitted conforming Petrov-Galerkin method. We identify norms for which we have both continuity and an…
A general system of n ordinary differential equations coupled with one reaction-diffusion equation, considered in a bounded N-dimensional domain, with no-flux boundary condition is studied in a context of pattern formation. Such initial…
We study the recently introduced notion of output-input stability, which is a robust variant of the minimum-phase property for general smooth nonlinear control systems. The subject of this paper is developing the theory of output-input…
This paper addresses the derivation of generic and tractable sufficient conditions ensuring the stability of a coupled system composed of a reaction-diffusion partial differential equation (PDE) and a finite-dimensional linear time…
In this paper we provide detailed information about the instability of equilibrium solutions of a nonlinear family of localized reaction-difussion equations in dimensione one. Beyond we provide explicit formulas to the equilibrium…
In this research note we provide a variational basis for the optimal artificial diffusion method, which has been a cornerstone in developing many stabilized methods. The optimal artificial diffusion method produces exact nodal solutions…
We study stability of the sharp Poincar{\'e} constant of the invariant probability measure of a reversible diffusion process satisfying some natural conditions. The proof is based on the spectral interpretation of Poincar{\'e} inequalities…
We provide some criteria on the stability of regime-switching diffusion processes. Both the state-independent and state-dependent regime-switching diffusion processes with switching in a finite state space and an infinite countable state…
Constrained diffusions in convex polyhedral domains with a general oblique reflection field, and with a diffusion coefficient scaled by a small parameter, are considered. Using an interior Dirichlet heat kernel lower bound estimate for…
Consider the one-dimensional stochastic Helmholtz equation where the source is assumed to be driven by the white noise. This paper concerns the stability analysis of the inverse random source problem which is to reconstruct the statistical…
The role of the electron diffusion on the stability of a Townsend discharge is investigated. It is obtained, that electron diffusion modifies the condition of the steady self-sustenance of the discharge, and make discharge unstable.
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…
Prolongating our previous paper on the Einstein relation, we study the motion of a particle diffusing in a random reversible environment when subject to a small external forcing. In order to describe the long time behavior of the particle,…
A quasi-two-dimensional system of hard spheres strongly confined between two parallel plates is considered. The attention is focussed on the macroscopic self-diffusion process observed when the system is looked from above or from below. The…
The paper studies the output-feedback synchronization problem for a network of identical, linear time-invariant systems. A criterion to test network synchronization is derived and the class of output-feedback synchronizable systems is…
We establish necessary and sufficient conditions for stochastic invariance of closed subsets in Hilbert spaces for solutions to infinite-dimensional stochastic differential equations (SDEs) under mild assumptions on the coefficients. Our…
Divergence and vorticity damping, which operate upon horizontal divergence and relative vorticity, are explicit diffusion mechanisms used in dynamical cores to ensure stability. To avoid numerical blow-up from excessively strong diffusion,…
This paper is concerned with the stability issue in determining absorption and diffusion coefficients in quantitative photoacoustic imaging. Assuming that the optical wave is generated by point sources in a region where the optical…