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Numerical meshes ensuring uniform observability of one-dimensional waves: Construction and analysis
(2016-01-01)
We build nonuniform numerical meshes for the finite difference and finite element approximations of the one-dimensional wave equation, ensuring that all numerical solutions reach the boundary, as continuous solutions do, ...
Control of 2D scalar conservation laws in the presence of shocks
(2016-01-01)
We analyze a model optimal control problem for a 2D scalar conservation law-the so-called inverse design problem-with the goal being to identify the initial datum leading to a given final time configuration. The presence ...
Optimal strategies for driving a mobile agent in a "guidance by repulsion" model
(2016-01-01)
We present a guidance by repulsion model based on a driver-evader interaction where the driver, assumed to be faster than the evader, follows the evader but cannot be arbitrarily close to it, and the evader tries to move ...
Null controllability for a heat equation with a singular inverse-square potential involving the distance to the boundary function
(2016-01-01)
This article is devoted to the analysis of control properties for a heat equation with a singular potential μ/δ2, defined on a bounded C2 domain Ω⊂RN, where δ is the distance to the boundary function. More precisely, we ...
Dispersion for 1-d Schrödinger and wave equations with bv coefficients
(2016-01-01)
In this paper we analyze the dispersion for one dimensional wave and Schrödinger equations with BV coefficients. In the case of the wave equation we give a complete answer in terms of the variation of the logarithm of the ...
Optimal Shape and Location of Sensors for Parabolic Equations with Random Initial Data
(2015-12-31)
In this article, we consider parabolic equations on a bounded open connected subset Rn. We model and investigate the problem of optimal shape and location of the observation domain having a prescribed measure. This problem ...
Complexity and regularity of maximal energy domains for the wave equation with fixed initial data
(2015-12-31)
We consider the homogeneous wave equation on a bounded open connected subset Ω of IRn. Some initial data being specified, we consider the problem of determining a measurable subset ω of Ω maximizing the L2-norm of the ...
Numerical approximation schemes for multi-dimensional wave equations in asymmetric spaces
(2015-12-31)
We develop finite difference numerical schemes for a model arising in multi-body structures, previously analyzed by H. Koch and E. Zuazua, constituted by two n-dimensional wave equations coupled with a (n - 1)- dimensional ...
Sparse initial data identification for parabolic PDE and its finite element approximations
(2015-12-31)
We address the problem of inverse source identication for parabolic equations from the optimal control viewpoint employing measures of minimal norm as initial data. We adopt the point of view of approximate controllability ...
Numerical aspects of large-time optimal control of Burgers equation
(2015-10-13)
In this paper, we discuss the efficiency of various numerical methods for the inverse design of the Burgers equation, both in the viscous and in the inviscid case, in long time-horizons. Roughly, the problem consists in, ...