## Diff. Equa. & Dyna. Sys.

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#### Trends in Control and Inverse Problems

By Kaïs Ammari and Stéphane Gerbi

ISBN-10: 1-60133-021-9

ISBN-13: 978-1-60133-021-5

This volume is dedicated to recent trends in Control and Inverse problems. It is constituted of two courses and three research papers.

The first mini-course topic is “Controllability of some evolution equations by the flatness approach”. This recent point of view on the controllability of partial differential equations permits to decide whether a system may be controllable and most of all it permits to design explicit controls. This course constitutes the first part of this volume.

The second mini-course topic is “Identification of mono- and multi-color inclusions”. This course is devoted to methods to detect inclusions in a 2D motive and is mainly concerns with inverse and optimization problem.

Research papers treat of:

1) the reconstructions from boundary measurements where the author is particularly interested in methods using minimal observations of the solution on the boundary.

2) the stability of a transmission problem, coupling a string (wave equation) and a beam (Euler Bernoulli equation) in one dimension. The author treats two cases. In the first, a control feedback is applied at one of the external nodes and in the second, one of the two elastic components is supposed to be thermoelastic. Some results of exponential and polynomial stability are established by a technique based on a frequency domain method.

3) the semi-classical structure of the interior Dirichlet-to-Neumann map for an arbitrary bounded domain with a non- empty smooth boundary.

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