arXiv subjects

R. Lecaros

Publications and source records attributed to R. Lecaros.

4 recordsLinked to original sources

arXiv2024

Controllability for a non-local formulation of surface gravity waves

In this paper, we study the approximate controllability of a system governed by an evolution problem known as the sloshing problem. This problem involves a spatial, nonlocal differential operator inherent in the dynamics of a two-dimensional, incompressible, non-viscous fluid within a confined domain. Our work establishes unique continuation results that enable the application of source control localized in an interior domain, allowing the aforementioned controllability.

math.AP↗

arXiv2020

The stability for an inverse problem of bottom recovering in water-waves

In this article we deal with a class of geometric inverse problem for bottom detection by one single measurement on the free surface in water--waves. We found upper and lower bounds for the size of the region enclosed between two different bottoms, in terms of Neumann and/or Dirichlet data on the free surface. Starting from the general water--waves system in bounded domains with side walls, we manage to formulate the problem in terms of the Dirichlet to Neumann operator and thus, as an elliptic problem in a bounded domain with Neumann homogeneous condition on the rigid boundary. Then we study the properties of the Dirichlet to Neumann map and analyze the called method of size estimation.

math.AP↗

arXiv2016

Predictive Index for slope instabilities in open pit mining

In this paper we study the stability and deformation of structures, in particular the wall of an open pit mine is studied by using information obtained from a variety of remote sensors and some extra data, with a novelty approach considering the use of mathematical models and data mining techniques. In particular we present two models to help the study the slope stability of pit and the possible occurrence of movements. Primarily we present an static model for slow movements, which will help us identify areas of possible risks areas with time horizons of several months or years, depends on the available information, before the wall start moving, and secondly a dynamic short-term model, which help us to determine risks of collapse zones with several days in advance. We remark that this methodology can be a powerful tool to plain future actions in order to simulate possible scenarios considering the production plans.

physics.geo-ph↗

arXiv2013

Determination of the calcium channel distribution in the olfactory system

In this paper we study a linear inverse problem with a biological interpretation, which is modeled by a Fredholm integral equation of the first kind. When the kernel in the Fredholm equation is represented by step func- tions, we obtain identifiability, stability and reconstruction results. Further- more, we provide a numerical reconstruction algorithm for the kernel, whose main feature is that a non-regular mesh has to be used to ensure the invert- ibility of the matrix representing the numerical discretization of the system. Finally, a second identifiability result for a polynomial approximation of degree less than nine of the kernel is also established.

math.OC↗