Zobrazeno 1 - 10
of 68
pro vyhledávání: '"Duca, Alessandro"'
In this work we analyse the small-time reachability properties of a nonlinear parabolic equation, by means of a bilinear control, posed on a torus of arbitrary dimension $d$. Under a saturation hypothesis on the control operators, we show the small-t
Externí odkaz:
http://arxiv.org/abs/2407.10521
We study composite assemblages of dielectrics and metamaterials with respectively positive and negative material parameters. In the continuum case, for a scalar equation, such media may exhibit so-called plasmonic resonances for certain values of the
Externí odkaz:
http://arxiv.org/abs/2407.06661
Autor:
Buffe, Rémi, Duca, Alessandro
The exact controllability of heat type equations in the presence of bilinear controls have been successfully studied in the recent works [1,3,14] motivated by the numerous application to engineering, neurobiology, chemistry, and life science. Neverth
Externí odkaz:
http://arxiv.org/abs/2406.17348
Autor:
Duca, Alessandro, Pozzoli, Eugenio
We address the small-time controllability problem for a nonlinear Schr\"odinger equation (NLS) on $\mathbb{R}^N$ in the presence of magnetic and electric external fields. We choose a particular framework where the equation becomes $i\partial_t \psi =
Externí odkaz:
http://arxiv.org/abs/2307.15819
The aim of this work is to study the controllability of the Schr\"odinger equation \begin{equation}\label{eq_abstract} i\partial_t u(t)=-\Delta u(t)~~~~~\text{ on }\Omega(t) \tag{$\ast$} \end{equation} with Dirichlet boundary conditions, where $\Omeg
Externí odkaz:
http://arxiv.org/abs/2203.00486
Autor:
Duca, Alessandro, Nersesyan, Vahagn
We consider the 1D nonlinear Schr\"odinger equation with bilinear control. In the case of Neumann boundary conditions, local exact controllability of this equation near the ground state has been proved by Beauchard and Laurent in arXiv:1001.3288. In
Externí odkaz:
http://arxiv.org/abs/2202.08723
Partial differential equation on networks have been widely investigated in the last decades in view of their application to quantum mechanics (Schr\"odinger type equations) or to the analysis of flexible structures (wave type equations). Nevertheless
Externí odkaz:
http://arxiv.org/abs/2111.02250
Autor:
Duca, Alessandro, Castro, Carlos
In this work, we study the Schr\"odinger equation $i\partial_t\psi=-\Delta\psi+\eta(t)\sum_{j=1}^J\delta_{x=a_j(t)}\psi$ on $L^2((0,1),C)$ where $\eta:[0,T]\longrightarrow R^+$ and $a_j:[0,T]\longrightarrow (0,1)$, $j=1,...,J$. We show how to permute
Externí odkaz:
http://arxiv.org/abs/2107.03929
Autor:
Duca, Alessandro, Nersesyan, Vahagn
We consider the nonlinear Schr\"odinger equation (NLS) on a torus of arbitrary dimension. The equation is studied in presence of an external potential field whose time-dependent amplitude is taken as control. Assuming that the potential satisfies a s
Externí odkaz:
http://arxiv.org/abs/2101.12103
Autor:
Duca, Alessandro, Joly, Romain
We consider the Schr\''odinger equation \begin{equation}\label{eq_abstract} i\partial_t u(t)=-\Delta u(t)~~~~~\text{ on }\Omega(t) \tag{$\ast$} \end{equation}where $\Omega(t)\subset\mathbb{R}$ is a moving domain depending on the time $t\in [0,T]$. Th
Externí odkaz:
http://arxiv.org/abs/2006.02082