Ebook: Optimization in Elliptic Problems with Applications to Mechanics of Deformable Bodies and Fluid Mechanics
Author: William G. Litvinov (auth.)
- Tags: Mathematics general
- Series: Operator Theory: Advances and Applications 119
- Year: 2000
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- pdf
This book is intended to be both a thorough introduction to contemporary research in optimization theory for elliptic systems with its numerous applications and a textbook at the undergraduate and graduate level for courses in pure or applied mathematics or in continuum mechanics. Various processes of modern technology and production are described by el liptic partial differential equations. Optimization of these processes reduces to op timization problems for elliptic systems. The numerical solution of such problems is associated with the solution of the following questions. 1. The setting of the optimization problem ensuring the existence of a solution on a set of admissible controls, which is a subset of some infinite-dimensional vector space. 2. Reduction of the infinite-dimensional optimization problem to a sequence of finite-dimensional problems such that the solutions of the finite-dimensional problems converge, in a sense, to the solution of the infinite-dimensional problem. 3. Numerical solution of the finite-dimensional problems.
This book is unique in that it presents a profound mathematical analysis of general optimization problems for elliptic systems, which are then applied to a great number of optimization problems in mechanics and technology. After the setting of a problem, attention is focused on existence theorems that lead to the construction of approximate solutions. The coefficients of the equations, the shape of the domain, and the right-hand sides of the equations are considered to be controls. Applications include optimization problems arising in mechanics of elastic solids, plates, shells, composite materials and structures fabricated with them, as well as fluid mechanics.
The monograph is written in an accessible and self-contained manner. It will be of interest to research mathematicians and science engineers working in solid and fluid mechanics, and in optimization theory of partial differential equations. Moreover, it is suitable as a textbook for graduate courses in optimization of elliptic systems.
This book is unique in that it presents a profound mathematical analysis of general optimization problems for elliptic systems, which are then applied to a great number of optimization problems in mechanics and technology. After the setting of a problem, attention is focused on existence theorems that lead to the construction of approximate solutions. The coefficients of the equations, the shape of the domain, and the right-hand sides of the equations are considered to be controls. Applications include optimization problems arising in mechanics of elastic solids, plates, shells, composite materials and structures fabricated with them, as well as fluid mechanics.
The monograph is written in an accessible and self-contained manner. It will be of interest to research mathematicians and science engineers working in solid and fluid mechanics, and in optimization theory of partial differential equations. Moreover, it is suitable as a textbook for graduate courses in optimization of elliptic systems.
Content:
Front Matter....Pages i-xxii
Basic Definitions and Auxiliary Statements....Pages 1-79
Optimal Control by Coefficients in Elliptic Systems....Pages 81-176
Control by the Right-hand Sides in Elliptic Problems....Pages 177-208
Direct Problems for Plates and Shells....Pages 209-286
Optimization of Deformable Solids....Pages 287-429
Optimization Problems for Steady Flows of Viscous and Nonlinear Viscous Fluids....Pages 431-501
Back Matter....Pages 503-522
This book is unique in that it presents a profound mathematical analysis of general optimization problems for elliptic systems, which are then applied to a great number of optimization problems in mechanics and technology. After the setting of a problem, attention is focused on existence theorems that lead to the construction of approximate solutions. The coefficients of the equations, the shape of the domain, and the right-hand sides of the equations are considered to be controls. Applications include optimization problems arising in mechanics of elastic solids, plates, shells, composite materials and structures fabricated with them, as well as fluid mechanics.
The monograph is written in an accessible and self-contained manner. It will be of interest to research mathematicians and science engineers working in solid and fluid mechanics, and in optimization theory of partial differential equations. Moreover, it is suitable as a textbook for graduate courses in optimization of elliptic systems.
Content:
Front Matter....Pages i-xxii
Basic Definitions and Auxiliary Statements....Pages 1-79
Optimal Control by Coefficients in Elliptic Systems....Pages 81-176
Control by the Right-hand Sides in Elliptic Problems....Pages 177-208
Direct Problems for Plates and Shells....Pages 209-286
Optimization of Deformable Solids....Pages 287-429
Optimization Problems for Steady Flows of Viscous and Nonlinear Viscous Fluids....Pages 431-501
Back Matter....Pages 503-522
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