Claude Zuily's Books

Tools and Problems in Partial Differential Equations

By: Thomas Alazard,Claude Zuily

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Tools and Problems in Partial Differential Equations

By: Thomas Alazard,Claude Zuily

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, Schrödinger 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.

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357

Publisher

Springer Nature

Published Date

ISBN 10

3030502848

ISBN 13

9783030502843

Carleman Estimates and Applications to Uniqueness and Control Theory

By: Feruccio Colombini,Claude Zuily

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Carleman Estimates and Applications to Uniqueness and Control Theory

By: Feruccio Colombini,Claude Zuily

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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232

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0817642307

ISBN 13

9780817642303

Strichartz Estimates and the Cauchy Problem for the Gravity Water Waves Equations

By: T. Alazard,N. Burq,C. Zuily

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Strichartz Estimates and the Cauchy Problem for the Gravity Water Waves Equations

By: T. Alazard,N. Burq,C. Zuily

This memoir is devoted to the proof of a well-posedness result for the gravity water waves equations, in arbitrary dimension and in fluid domains with general bottoms, when the initial velocity field is not necessarily Lipschitz. Moreover, for two-dimensional waves, the authors consider solutions such that the curvature of the initial free surface does not belong to L2. The proof is entirely based on the Eulerian formulation of the water waves equations, using microlocal analysis to obtain sharp Sobolev and Hölder estimates. The authors first prove tame estimates in Sobolev spaces depending linearly on Hölder norms and then use the dispersive properties of the water-waves system, namely Strichartz estimates, to control these Hölder norms.

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120

Publisher

American Mathematical Soc.

Published Date

ISBN 10

147043203X

ISBN 13

9781470432034

Tools and Problems in Partial Differential Equations

By: Thomas Alazard,Claude Zuily

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Tools and Problems in Partial Differential Equations

By: Thomas Alazard,Claude Zuily

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N/A

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Solve jigsaw puzzle

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Page Count

357

Publisher

Springer Nature

Published Date

ISBN 10

3030502848

ISBN 13

9783030502843

Book's by Claude Zuily

Tools and Problems in Partial Differential Equations

Tools and Problems in Partial Differential Equations

Carleman Estimates and Applications to Uniqueness and Control Theory

Carleman Estimates and Applications to Uniqueness and Control Theory

Strichartz Estimates and the Cauchy Problem for the Gravity Water Waves Equations

Strichartz Estimates and the Cauchy Problem for the Gravity Water Waves Equations

Tools and Problems in Partial Differential Equations

Tools and Problems in Partial Differential Equations

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