Related papers: Large-time optimal observation domain for linear p…
We construct a four-dimensional diffeomorphism exhibiting a homoclinic tangency of the largest codimension, which admits a historic wandering domain of positive Lebesgue measure. Every orbit in this wandering domain exhibits historic…
The maximum volume ($\Omega$) of a droplet that can remain attached to a horizontal fiber defines the stability limit of droplet-fiber interactions, phenomena common in nature and critical to diverse engineering applications. Existing…
In this work, we have considered the flat FRW model of the universe in $(n+2)$-dimensions filled with the dark matter and the magnetic field. We present the Hubble parameter in terms of the observable parameters $\Omega_{m0}$ and $H_{0}$…
We use some of the recently released observational data to test the viability of two classes of minimally coupled scalar field models of quintessence with exponential potentials for which exact solutions of the Einstein equations are known.…
Our goal is to study controllability and observability properties of the 1D heat equation with internal control (or observation) set $\omega_{\varepsilon}=(x_{0}-\varepsilon, x_{0}+\varepsilon )$, in the limit $\varepsilon\rightarrow 0$,…
One possibility for explaining the apparent accelerating expansion of the universe is that we live in the center of a spherically inhomogeneous universe. Although current observations cannot fully distinguish $\Lambda$CDM and these…
Recent observational results suggest that our universe is nearly flat and well modelled within a $\Lambda$CDM framework. The observed values of $\Omega_{m}$ and $\Omega_{\Lambda}$ inevitably involve uncertainties. Motivated by this, we make…
The discussion is limited to first-class parametrized systems, where the definition of time evolution and observables is not trivial, and to finite dimensional systems in order that technicalities do not obscure the conceptual framework.…
Let $\Omega\subset{\mathbb R}^2$ be a bounded domain on which Hardy's inequality holds. We prove that $[\exp(u^2)-1]/\delta^2\in L^1(\Omega)$ if $u\in H^1_0(\Omega)$, where $\delta$ denotes the distance to $\partial\Omega$. The…
The aim of this paper is to extend the concept of regional exponential general observability to the case of Neumann boundary conditions problem in diffusion system. More precisely, for linear distributed parameter diffusion systems, we show…
In this paper we consider a tank containing fluid and we want to estimate the horizontal currents when the fluid surface height is measured. The fluid motion is described by shallow water equations in two horizontal dimensions. We build a…
This paper deals with the observer design problem for time-varying linear infinite-dimensional systems. We address both the problem of online estimation of the state of the system from the output via an asymptotic observer, and the problem…
Sufficient conditions characterizing the asymptotic stability and the hybrid $L_1/\ell_1$-gain of linear positive impulsive systems under minimum and range dwell-time constraints are obtained. These conditions are stated as…
We start by reviewing recent probabilistic results on ergodic sums in a large class of (non-uniformly) hyperbolic dynamical systems. Namely, we describe the central limit theorem, the almost-sure convergence to the gaussian and other stable…
A well-known boundary observability inequality for the elasticity system establishes that the energy of the system can be estimated from the solution on a sufficiently large part of the boundary for a sufficiently large time. This…
In this article we consider the ergodic optimization for hyperbolic flows and Lorenz attractors with respect to both continuous and Holder continuous observables. In the context of hyperbolic flows we prove that a Baire generic subset of…
The dynamical behaviour of many-body systems is often richer than what can be anticipated from their static properties. Here we show that in closed quantum systems this becomes evident by considering time-integrated observables as order…
This paper is concerned with a partially observed hybrid optimal control problem, where continuous dynamics and discrete events coexist and in particular, the continuous dynamics can be observed while the discrete events, described by a…
We consider a $n \times n$ nonlinear reaction-diffusion system posed on a smooth bounded domain $\Omega$ of $\mathbb{R}^N$. This system models reversible chemical reactions. We act on the system through $m$ controls ($1 \leq m < n$),…
In this paper we study the geometry and the topology of unbounded domains in the Hyperbolic Space $\mathbb{H} ^n$ supporting a bounded positive solution to an overdetermined elliptic problem. Under suitable conditions on the elliptic…