arXiv subjects

Ademir Pazoto

Publications and source records attributed to Ademir Pazoto.

3 recordsLinked to original sources

arXiv2014

Internal controllability of the Korteweg-de Vries equation on a bounded domain

This paper is concerned with the control properties of the Korteweg-de Vries (KdV) equation posed on a bounded interval with a distributed control. When the control region is an arbitrary open subdomain, we prove the null controllability of the KdV equation by means of a new Carleman inequality. As a consequence, we obtain a regional controllability result, the state function being controlled on the left part of the complement of the control region. Finally, when the control region is a neighborhood of the right endpoint, an exact controllability result in a weighted L2 space is also established.

math.AP↗

arXiv2013

Large time behaviour for a nonlocal diffusion - convection equation related with the gas dynamics

In this paper we consider a model that involves nonlocal diffusion and a classical convective term. Using a scaling argument and a new compactness argument we obtain the first term in the asymptotic behavior of the solutions.

math.AP↗

arXiv2010

Uniform stabilization in weighted Sobolev spaces for the KdV equation posed on the half-line

Studied here is the large-time behavior of solutions of the Korteweg-de Vries equation posed on the right half-line under the effect of a localized damping. Assuming as in \cite{linares-pazoto} that the damping is active on a set $(a_0,+\infty)$ with $a_0>0$, we establish the exponential decay of the solutions in the weighted spaces $L^2((x+1)^mdx)$ for $m\in \N ^*$ and $L^2(e^{2bx}dx)$ for $b>0$ by a Lyapunov approach. The decay of the spatial derivatives of the solution is also derived.

math.AP↗