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Control and inverse problems for partial differential equations

Author: Gang Bao; Jean-Michel Coron; Daqian Li
Publisher: Beijing, China : Higher Education Press Limited Company ; Singapore ; Hackensack, NJ : World Scientific Publishing Co. Pte. Ltd., [2019]
Series: Series in contemporary applied mathematics, 22.
Edition/Format:   eBook : Document : EnglishView all editions and formats
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Genre/Form: Electronic books
Additional Physical Format: Print version:
(OCoLC)1047785383
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Gang Bao; Jean-Michel Coron; Daqian Li
ISBN: 9789813276154 9813276150
OCLC Number: 1100449666
Description: 1 online resource
Contents: Intro; Contents; Preface; Control of Partial Differential Equations: Theoretical Aspects; 1. Introduction; 2. Introduction to Controllability; 2.1. Approximate Controllability; 2.2. Null Controllability; 2.3. Exact Controllability; 2.4. Exact Controllability to Trajectories; 3. Simple Examples; 3.1. Transport Equation in 1-D; 3.2. Wave Equation in 1-D; 4. Exact Controllability for the Wave Equation; 4.1. Exact Controllability for Boundary Control; 4.2. Case of Distributed Control; 5. Controllability of Schrödinger Equation; 5.1. Schrödinger Equation; 5.2. Controllability Results 6. Controllability of Linear Diffusion Convection Equations6.1. Statement of the Problem and Result; 6.2. An Auxiliary Optimal Control Problem; 6.3. Null Controllability Modulo Observability Inequality; 6.4. Global Carleman Inequality; 6.4.1. Weight Functions; 6.4.2. Proof of a Global Carleman Inequality; 6.4.3. Case of a General Diffusion-Convection Operator; 6.5. Observability Inequality; 6.6. Another Strategy; Bibliography; Control of Partial Differential Equations: Numerical Aspects; 1. Introduction; 2. Controllability of Finite-Dimensional Linear Systems; 2.1. Introduction 2.2. Finite-Dimensional Case, First Comments2.3. Examples; 2.4. Duality Techniques; 2.5. Observability Property; 2.6. Comments on the Control Map; 2.7. Kalman Rank Condition; 2.8. A Data Assimilation Problem; 3. The Wave Equation; 3.1. The Continuous Setting; 3.1.1. Functional Setting; 3.1.2. Control and Observability Results; 3.2. The Discrete Wave Equation: The Naive Approach; 3.2.1. Setting; 3.2.2. Existence of the Discrete Null-Controls; 3.2.3. Numerical Experiments; 3.2.4. Lack of Uniform Observability; 3.2.5. Blow up of Discrete Controls; 3.3. Remedies 3.3.1. A Fourier Filtering Technique3.3.2. Designing a Mesh Guaranteeing Uniform Observability Properties; 3.4. Further Comments; 3.4.1. Higher Dimensions; 3.4.2. The Effect of Time-Discretization; 3.4.3. Rate of Convergence of the Discrete Controls; 4. The Heat Equation; 4.1. The Continuous Case; 4.2. Difficulties of Computing Numerical Controls for the Heat Equation; 4.3. A Remedy; 4.4. Further Comments; Bibliography; Complex Geometrical Optics and Calderón's Problem; 0. Introduction; 1. The Dirichlet-to-Neumann Map; 2. Boundary Determination and Layer Stripping 3. Complex Geometrical Optics Solutions4. Applications of Complex Geometrical Optics Solutions; 4.1. Uniqueness for Calderón's Problem; 4.2. Determining Cavities; 5. Complex Geometrical Optics Solutions for First Order Perturbations of the Laplacian; 5.1. Intertwining Property (Part 1); 5.2. Intertwining Property (Part 2); 5.3. Intertwining Property (Part 3) --
Some Reductions; 5.4. Construction of Pseudoanalytic Matrices; Bibliography; A Mini-Course on Stochastic Control; 1. Introduction; 2. Some Preliminary Results from Probability Theory and Stochastic Analysis
Series Title: Series in contemporary applied mathematics, 22.
Responsibility: editors Gang Bao, Jean-Michel Coron, Tatsien Li.

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