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Numerical Estimations of the Cost of Boundary Controls for the Equation ytεyxx + Myx = 0 with Respect to ε

  • Arnaud MünchEmail author
Chapter
Part of the SEMA SIMAI Springer Series book series (SEMA SIMAI, volume 17)

Abstract

We numerically examine the cost of the null boundary control for the transport diffusion equation yt − εyxx + Myx = 0, x ∈ (0, L), t ∈ (0, T) with respect to the positive parameter ε. It is known that this cost is uniformly bounded with respect to ε if T ≥ TM with \(T_M\in [1, 2\sqrt {3}]L/M\) if M > 0 and if \(T_M\in [2\sqrt {2},2(1+\sqrt {3})]L/\vert M\vert \) if M < 0. We propose a method to approximate the underlying observability constant and then conjecture, through numerical computations, the minimal time of controllability TM leading to a uniformly bounded cost. Several experiments for M ∈{−1, 1} are performed and discussed.

Keywords

Singular controllability Lagrangian variational formulation Numerical approximation 

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques Blaise PascalUniversité Clermont Auvergne, UMR CNRS 6620AubièreFrance

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