| Description |
1 online resource (306 pages) |
| Contents |
Cover; Title Page; Copyright Page; Dedication; Table of Contents; Chapter 1. Principles of construction of adjoint operators in non-linear problems; 1. Dual spaces and adjoint operators; 2. Construction of adjoint operators based on using the Lagrange identity; 3. Definition of adjoint operators based on using Taylor's formula; 4. Operators of the class D and their adjoint operators; Chapter 2. Properties of adjoint operators constructed on the basis of various principles; 1. General properties of main and adjoint operators corresponding to non-linear operators |
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2. Properties of operators of the class D3. Properties of adjoint operators constructed with the use of the Taylor formula; Chapter 3. Solvability of main and adjoint equations in non-linear problems; 1. Main and adjoint equations. Problems; 2. Solvability of the equation F(u) = y; 3. Solvability of the equation A(u) v = y; 4. Solvability of the equation Ã(u) v = y; 5. Solvability of the equation A*(u) w = p; 6. Solvability of the equation Ã*(u) w = p; Chapter 4. Transformation groups, conservation laws and constructing the adjoint operators in non-linear problems |
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1. Definitions. Non-linear equations and operators. Conservation laws2. Transformation of equations; 3. Adjoint equations; 4. Relationship between different adjoint operators; 5. General remarks on constructing the adjoint equations with the use of the Lie groups and conservation laws; 6. Construction of adjoint operators with prescribed properties; 7. The Noether theorem, conservation laws and adjoint operators; 8. On some applications of adjoint equations; Chapter 5. Perturbation algorithms in non-linear problems |
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1. Perturbation algorithms for original non-linear equations and equations involving adjoint operators2. Perturbation algorithms for non-linear functionals based on using main and adjoint equations; 3. Spectral method in perturbation algorithms; 4. Justification of the N-th order perturbation algorithms; 5. Convergence rate estimates for perturbation algorithms. Comparison with the successive approximation method; 6. Justification of perturbation algorithms in quasi-linear elliptic problems |
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Chapter 6. Adjoint equations and the N-th order perturbation algorithms in non-linear problems of transport theory1. Some problems of transport theory; 2. The N-th order perturbation algorithms for an eigenvalue problem; 3. A problem of control and its approximate solution with the use of perturbation algorithms; 4. Investigation and approximate solution of a non-linear problem for the transport equation; Chapter 7. Adjoint equations and perturbation algorithms for a quasilinear equation of motion; 1. Statement of the problem. Basic assumptions. Operator formulation |
| Notes |
2. Transformation of the problem. Properties of the non-linear operator |
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Print version record |
| Form |
Electronic book
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| Author |
Agoshkov, Valeri I
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Shutyaev, Victor P
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| ISBN |
9781351468794 |
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1351468790 |
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