| Preface | |
| Introduction | |
| Basic Definitions and Auxiliary Statements | |
| Sets, functions, real numbers | p. 1 |
| Topological, metric, and normed spaces | p. 4 |
| Continuous functions and compact spaces | p. 10 |
| Maximum function and its properties | p. 14 |
| Hilbert space | p. 17 |
| Functional spaces that are used in the investigation of boundary value and optimal control problems | p. 36 |
| Inequalities of coerciveness | p. 44 |
| Theorem on the continuity of solutions of functional equations | p. 50 |
| Differentiation in Banach spaces and the implicit function theorem | p. 51 |
| Differentiation of the norm in the space W[subscript p][superscript m]([Omega]) | p. 54 |
| Differentiation of eigenvalues | p. 58 |
| The Lagrange principle in smooth extremum problems | p. 70 |
| G-convergence and G-closedness of linear operators | p. 72 |
| Diffeomorphisms and invariance of Sobolev spaces with respect to diffeomorphisms | p. 73 |
| Optimal Control by Coefficients in Elliptic Systems | |
| Direct problem | p. 81 |
| Optimal control problem | p. 86 |
| The finite-dimensional problem | p. 103 |
| The finite-dimensional problem (another approach) | p. 105 |
| Spectral problem | p. 117 |
| Optimization of the spectrum | p. 120 |
| Control under restrictions on the spectrum | p. 129 |
| The basic optimal control problem | p. 138 |
| The combined problem | p. 142 |
| Optimal control problem for the case when the state of the system is characterized by a set functions | p. 145 |
| The general control problem | p. 149 |
| Optimization by the shape of domain and by operators | p. 159 |
| Optimization problems with smooth solutions of state equations | p. 168 |
| Control by the Right-hand Sides in Elliptic Problems | |
| On the minimum of nonlinear functionals | p. 177 |
| Approximate solution of the minimization problem | p. 183 |
| Control by the right-hand side in elliptic problems provided the goal functional is quadratic | p. 191 |
| Minimax control problems | p. 198 |
| Control of systems whose state is described by variational inequalities | p. 201 |
| Direct Problems for Plates and Shells | |
| Bending and free oscillations of thin plates | p. 209 |
| Problem of stability of a thin plate | p. 223 |
| Model of the three-layered plate ignoring shears in the middle layer | p. 242 |
| Model of the three-layered plate accounting for shears in the middle layer | p. 246 |
| Basic relations of the shell theory | p. 257 |
| Shells of revolution | p. 260 |
| Shallow shells | p. 265 |
| Problems of statics of shells | p. 267 |
| Free oscillations of a shell | p. 268 |
| Problem of shell stability | p. 270 |
| Finite shear model of a shell | p. 274 |
| Laminated shells | p. 282 |
| Optimization of Deformable Solids | |
| Settings of optimization problems for plates and shells | p. 287 |
| Approximate solution of direct and optimization problems for plates and shells | p. 291 |
| Optimization problems for plates (control by the function of the thickness) | p. 300 |
| Optimization problems for shells (control by functions of midsurface and thickness) | p. 312 |
| Control by the shape of a hole and by the function of thickness for a shallow shell | p. 319 |
| Control by the load for plates and shells | p. 326 |
| Optimization of structures of composite materials | p. 333 |
| Optimization of laminate composite covers according to mechanical and radio engineering characteristics | p. 373 |
| Shape optimization of a two-dimensional elastic body | p. 383 |
| Optimization of the Internal boundary of a two-dimensional elastic body | p. 388 |
| Optimization problems on manifolds and shape optimization of elastic solids | p. 391 |
| Optimization of the residual stresses in an elastoplastic body | p. 409 |
| Optimization Problems for Steady, Flows of Viscous and Nonlinear Viscous Fluids | |
| Problem of steady flow of a nonlinear viscous fluid | p. 431 |
| Theorem on continuity | p. 443 |
| Continuity with respect to the shape of the domain | p. 446 |
| Control of fluid flows by perforated walls and computation of the function of filtration | p. 454 |
| The flow in a canal with a perforated wall placed inside | p. 460 |
| Optimization by the functions of surface forces and filtration | p. 463 |
| Problems of the optimal shape of a canal | p. 471 |
| A problem of the optimal shape of a hydrofoil | p. 478 |
| Direct and optimization problems with consideration for the inertia forces | p. 495 |
| Bibliography | p. 503 |
| Index | p. 519 |
| Table of Contents provided by Blackwell. All Rights Reserved. |
