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The articles in this volume reflect a subsequent development after
a scientific meeting entitled Carleman Estimates and Control
Theory, held in Cartona in September 1999. The 14 research-level
articles, written by experts, focus on new results on Carleman
estimates and their applications to uniqueness and controlla-
bility of partial differential equations and systems. The main
topics are unique continuation for elliptic PDEs and systems, con-
trol theory and inverse problems. New results on strong uniqueness
for second or higher order operators are explored in detail in
several papers. In the area of control theory. the reader will find
applications of Carleman estimates to stabiliza- tion,
observability and exact control for the wave and the SchrOdinger
equations. A final paper presents a challenging list of open
problems on the topic of control- lability of linear and
sernilinear heat equations. The papers contain exhaustive and
essentially self-contained proofs directly ac- cessible to
mathematicians, physicists, and graduate students with an
elementary background in PDEs. Contributors are L. Aloui, M.
Bellassoued, N. Burq, F. Colombini, B. Dehman, C. Grammatico, M.
Khenissi, H. Koch, P. Le Borgne, N. Lerner, T. Nishitani. T. Okaji,
K.D. Phung, R. Regbaoui, X. Saint Raymond, D. Tataru, and E.
Zuazua.
This textbook offers a unique learning-by-doing introduction to the
modern theory of partial differential equations.Through 65 fully
solved problems, the book offers readers a fast but in-depth
introduction to the field, covering advanced topics in microlocal
analysis, including pseudo- and para-differential calculus, and the
key classical equations, such as the Laplace, Schroedinger or
Navier-Stokes equations. Essentially self-contained, the book
begins with problems on the necessary tools from functional
analysis, distributions, and the theory of functional spaces, and
in each chapter the problems are preceded by a summary of the
relevant results of the theory. Informed by the authors' extensive
research experience and years of teaching, this book is for
graduate students and researchers who wish to gain real working
knowledge of the subject.
The articles in this volume reflect a subsequent development after
a scientific meeting entitled Carleman Estimates and Control
Theory, held in Cartona in September 1999. The 14 research-level
articles, written by experts, focus on new results on Carleman
estimates and their applications to uniqueness and controlla-
bility of partial differential equations and systems. The main
topics are unique continuation for elliptic PDEs and systems, con-
trol theory and inverse problems. New results on strong uniqueness
for second or higher order operators are explored in detail in
several papers. In the area of control theory. the reader will find
applications of Carleman estimates to stabiliza- tion,
observability and exact control for the wave and the SchrOdinger
equations. A final paper presents a challenging list of open
problems on the topic of control- lability of linear and
sernilinear heat equations. The papers contain exhaustive and
essentially self-contained proofs directly ac- cessible to
mathematicians, physicists, and graduate students with an
elementary background in PDEs. Contributors are L. Aloui, M.
Bellassoued, N. Burq, F. Colombini, B. Dehman, C. Grammatico, M.
Khenissi, H. Koch, P. Le Borgne, N. Lerner, T. Nishitani. T. Okaji,
K.D. Phung, R. Regbaoui, X. Saint Raymond, D. Tataru, and E.
Zuazua.
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