The main topics are unique continuation for elliptic PDEs and systems, control 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 stabilization, observability and exact control for the wave and Schrödinger equations. A final paper presents a challenging list of open problems on the topic of controllability of linear and semilinear heat equations.
The articles contain exhaustive and essentially self-contained proofs directly accessible to mathematicians, physicists, and graduate students with an elementary background in PDEs.
Contributors: 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, E. Zuazua
|Series:||Progress in Nonlinear Differential Equations and Their Applications , #46|
|Edition description:||Softcover reprint of the original 1st ed. 2001|
|Product dimensions:||6.10(w) x 9.25(h) x 0.02(d)|
Table of ContentsPreface * 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 Gårding 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 Schrödinger 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