Adjoint Equations and Perturbation Algorithms in Nonlinear Problems

Guri I. Marchuk, Valeri I. Agoshkov, Victor P. Shutyaev

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English

CRC Press
30 June 2020

Differential calculus & equations; Applied mathematics

Sparked by demands inherent to the mathematical study of pollution, intensive industry, global warming, and the biosphere, Adjoint Equations and Perturbation Algorithms in Nonlinear Problems is the first book ever to systematically present the theory of adjoint equations for nonlinear problems, as well as their application to perturbation algorithms. This new approach facilitates analysis of observational data, the application of adjoint equations to retrospective study of processes governed by imitation models, and the study of computer models themselves. Specifically, the book discusses:

Principles for constructing adjoint operators in nonlinear problems

Properties of adjoint operators and solvability conditions for adjoint equations

Perturbation algorithms using the adjoint equations theory for nonlinear problems in transport theory, quasilinear motion, substance transfer, and nonlinear data assimilation

Known results on adjoint equations and perturbation algorithms in nonlinear problems

This groundbreaking text contains some results that have no analogs in the scientific literature, opening unbounded possibilities in construction and application of adjoint equations to nonlinear problems of mathematical physics.

By: Guri I. Marchuk, Valeri I. Agoshkov, Victor P. Shutyaev
Imprint: CRC Press
Country of Publication: United Kingdom
Dimensions: Height: 234mm, Width: 156mm,
Weight: 640g
ISBN: 9780367448585
ISBN 10: 0367448580
Pages: 288
Publication Date: 30 June 2020
Audience: College/higher education , Primary
Format: Paperback
Publisher's Status: Active

Principles of Construction of Adjoint Operators in Non-Linear Problems. Properties of Adjoint Operators Constructed on the Basis of Various Principles. Solvability of Main and Adjoint Equations in Non-Linear Problems. Transformation Groups, Conservation Laws and Construction of the Adjoint Operators in Non-Linear Problems. Perturbation Algorithms in Non-Linear Problems. Adjoint Equations and the N-th Order Perturbation Algorithms in Non-Linear Problems of Transport Theory. Adjoint Equations and Perturbation Algorithms for a Quasilinear Equation of Motion. Adjoint Equations and Perturbation Algorithms for a Non-Linear Mathematical Model of Mass Transfer in Soil. Applications of Adjoint Equations in Science and Technology. Backcover Copy

Marchuk, Guri I. | Agoshkov, Valeri I. | Shutyaev, Victor P.