Guri I. Marchuk – författare

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 problemsThis 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.

This monograph presents the fundamentals of adjoint equation theory and perturbation algorithms, exemplifying their applications by solutions of complex problems of mathematical physics. The earlier Russian version (1992) has been completely revised and supplemented with many new results for this edition, thus offering a unique compilation of the author's research in many areas of applied mathematics over the years. The first part of the book describes the theory of adjoint equations and perturbation algorithms and gives examples of applications to problems. Nonlinear problems and statements of inverse problems based on methods of adjoint equations and perturbation are considered. The second part focuses on the applications of adjoint equations theory and perturbation algorithms to the solution of concrete problems, such as global and regional environmental protection, interaction between atmosphere and ocean, and data assimilation problems.This volume should be of value to a wide range of researchers, workers and engineers interested in creating new technologies for designing and planning experiments, while solving concrete problems, especially for those working on numerical mathematics.

This monograph aims to present a unified approach to using mathematical models in the study of qualitative and quantitative regularities of immune response dynamics in infectious diseases within individual organisms. These mathematical models are formulated as systems of delay-differential equations. Simple mathematical models of infectious diseases, antiviral immune response and antibacterial response are developed and applied to the study of hepatitis B, influenza A, infectious bacterial pneumonia, and mixed infections. Particular attention is paid to the development of efficient computational procedures for solving the initial value problem for stiff delay-differential equations and to the parameter identification problem. Adjoint equations and the perturbation theory are used for the sensitivity analysis. This book is aimed at mathematicians and specialists in immunology and infectious diseases. It can also be used as a textbook for postgraduate students, bridging the gap between mathematics, immunology and infectious diseases research.

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 problemsThis 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.

This is the first monograph to present the fundamentals of adjoint equation theory and perturbation algorithms, exemplifying their applications by solutions of complex problems of mathematical physics. The earlier Russian version (1992) has been completely revised and supplemented with many new results for this edition, thus offering a unique compilation of the author's research in many areas of applied mathematics over the years. The first part of the book describes the theory of adjoint equations and perturbation algorithms and gives examples of applications to problems. Nonlinear problems and statements of inverse problems based on methods of adjoint equations and perturbation are considered. The second part focuses on the applications of adjoint equations theory and perturbation algorithms to the solution of concrete problems, such as global and regional environmental protection, interaction between atmosphere and ocean, and data assimilation problems.This volume will be of great value to a wide range of researchers, workers and engineers interested in creating new technologies for designing and planning experiments, while solving concrete problems, especially for those working on numerical mathematics.

This is the first monograph to present a unified approach to using mathematical models in the study of qualitative and quantitative regularities of immune response dynamics in infectious diseases within individual organisms. These mathematical models are formulated as systems of delay- differential equations. Simple mathematical models of infectious diseases, antiviral immune response and antibacterial response were developed and applied to the study of hepatitis B, influenza A, infectious bacterial pneumonia, and mixed infections. Particular attention was paid to the development of efficient computational procedures for solving the initial value problem for stiff delay-differential equations and to the parameter identification problem. Adjoint equations and the perturbation theory were used for the sensitivity analysis. Audience: This book will be of interest to a wide range of mathematicians and specialists in immunology and infectious diseases. It can also be recommended as a textbook for postgraduate students, bridging the gap between mathematics, immunology and infectious diseases research.