Carleman estimates and applications to uniqueness and control theory
著者
書誌事項
Carleman estimates and applications to uniqueness and control theory
（Progress in nonlinear differential equations and their applications / editor, Haim Brezis, 46）
Birkhäuser, c2001
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注記
Includes bibliographical references
内容説明・目次
内容説明
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.
目次
Preface * Stabilization for the Wave Equation on Exterior Domains / L. Aloui and M. Khenissi * Carleman Estimate and Decay Rate of the Local Energy for the Neumann Problem of Elasticity System / Bellassoued * Microlocal Effect Measures for Systems / N. Burq * Strong Uniqueness for Laplace and bi-Laplace Operators in Limit Case / F. Colombini and C. Grammatico * Stabilization for the Semilinear Wave Equation in Bounded Domain / B. Dehman * Recent Results on Unique Continuation for Second Order Elliptic Equations / H. Koch and D. Tataru * Strong Uniqueness for Fourth Order Elliptic Differential Operators / P. Le Borgne * Second Microlocalization Methods for Degenerate Cauchy--Riemann Equations / N. Lerner * A Garding Inequality on a Manifold with Boundary / N. Lerner and X. Saint Raymond * Some Necessary Conditions for Hyperbolic Systems / T. Nishitani * Strong Unique Continuation Property for First Order Elliptic Systems / T. Okaji * Observability of Schroedinger Equation / K.D. Phung * Unique Continuation from Sets of Positive Measure / R. Regbaoui * Some Results and Open Problems on the Controllability of Linear and Semilinear Heat Equations / E. Zuazua
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