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Symmetric discontinuous Galerkin approximations of waves: high frequency propagation and control
(2014-12-31)
This work describes the propagation properties of the so-called symmetric interior penalty discontinuous Galerkin (SIPG) approximations of the 1-d wave equation. This is done by means of linear approximations on uniform ...
Optimal sensor location for wave and Schrödinger equations
(2014-12-31)
This paper summarizes the research we have carried out recently on the problem of the optimal location of sensors and actuators for wave equa- tions, which has been the object of the talk of the third author at the Hyp2012 ...
Optimal shape and location of sensors or actuators in PDE models
(2014-12-31)
We investigate the problem of optimizing the shape and location of sensors and actuators for evolution systems driven by distributed parameter systems or partial differential equations (PDE). We consider wave, Schrödinger ...
Robust null controllability for heat equations with unknown switching control mode
(2014-12-31)
We analyze the null controllability for heat equations in the presence of switching controls. The switching pattern is a priori unknown so that the control has to be designed in a robust manner, based only on the past ...
Weak observability estimates for 1-D wave equations with rough coefficients
(2014-12-31)
In this paper we prove observability estimates for 1-dimensional wave equations with non-Lipschitz coefficients. For coefficients in the Zygmund class we prove a "classical" estimate, which extends the well-known observability ...
Propagation of 1D Waves in Regular Discrete Heterogeneous Media: A Wigner Measure Approach
(2014-12-31)
In this article, we describe the propagation properties of the one-dimensional wave and transport equations with variable coefficients semi-discretized in space by finite difference schemes on non-uniform meshes obtained ...
The turnpike property infinite-dimensional nonlinear optimal control
(2014-12-31)
Turnpike properties have been established long time ago in finite-dimensional optimal control problems arising in econometry. They refer to the fact that, under quite general assumptions, the optimal solutions of a given ...
Transmutation techniques and observability for time-discrete approximation schemes of conservative systems
(2014-12-31)
In this article, we consider abstract linear conservative systems and their time-discrete counterparts. Our main result is a representation formula expressing solutions of the continuous model through the solution of the ...
Large-time asymptotics, vanishing viscosity and numerics for 1-D scalar conservation laws
(2014-12-31)
In this paper we analyze the large time asymptotic behavior of the discrete solutions of numerical approximation schemes for scalar hyperbolic conservation laws. We consider three monotone conservative schemes that are ...
Averaged control
(2014-12-31)
We analyze the problem of controlling parameter-dependent systems. We introduce the notion of averaged control according to which the quantity of interest is the average of the states with respect to the parameter. First ...