arXiv subjects

R. Guglielmi

Publications and source records attributed to R. Guglielmi.

2 recordsLinked to original sources

arXiv2011

Indirect stabilization of weakly coupled systems with hybrid boundary conditions

We investigate stability properties of indirectly damped systems of evolution equations in Hilbert spaces, under new compatibility assumptions. We prove polynomial decay for the energy of solutions and optimize our results by interpolation techniques, obtaining a full range of power-like decay rates. In particular, we give explicit estimates with respect to the initial data. We discuss several applications to hyperbolic systems with {\em hybrid} boundary conditions, including the coupling of two wave equations subject to Dirichlet and Robin type boundary conditions, respectively.

math.OC↗

arXiv2011

Null controllability of Grushin-type operators in dimension two

We study the null controllability of the parabolic equation associated with the Grushin-type operator $A=\partial_x^2+|x|^{2γ}\partial_y^2\,, (γ>0),$ in the rectangle $Ω=(-1,1)\times(0,1)$, under an additive control supported in the strip $ω=(a,b)\times(0,1)\,, (0 1$. In the transition regime $γ=1$, we show that both behaviors live together: a positive minimal time is required for null controllability. Our approach is based on the fact that, thanks to the particular geometric configuration, null controllability is equivalent to the observability of the Fourier components of the solution of the adjoint system uniformly with respect to the frequency.

math.AP↗