Optimal control of partial differential equations : theory, methods, and applications / Fredi Troltzsch ; translated by Jürgen Sprekels

Contient des exercices

Bibliogr. p. 385-396. Index

Optimal control theory has found widespread applications in aeronautics, mechanical engineering, and many other disciplines. The book focuses on optimal control problems where the state equation is an elliptic or parabolic partial differential equation. Included are topics such as the existence of optimal solutions, necessary optimality conditions and adjoint equations, second-order sufficient conditions, and main principles of selected numerical techniques. It also contains a survey on the Karush-Kuhn-Tucker theory of nonlinear programming in Banach spaces.

To make the book self-contained, basic facts on weak solutions of PDEs are introduced. Principles of functional analysis are introduced and explained as they are needed. Many simple examples illustrate the theory. Advanced control problems for nonlinear PDEs are also discussed. As prerequisites, results on boundedness and continuity of solutions to semilinear elliptic and parabolic equations are addressed. These topics are not yet readily available in books on PDEs, making the exposition also interesting for researchers. Alongside the main theme of the analysis of problems of optimal control, the author also discusses numerical techniques. After reading this book, the reader will be familiar with the main principles of the numerical analysis of PDE-constrained optimization.

The book can be highly recommended to graduate students and research mathematicians interested in optimal control theory and PDEs. (Zentralblatt)