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Adjoint Equations and Analysis of Complex Systems

  • Book
  • © 1995

Overview

Authors:
  1. Guri I. Marchuk

    1. Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, Russia

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Part of the book series: Mathematics and Its Applications (MAIA, volume 295)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-ix
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  2. Introduction

    1. Introduction

      • Guri I. Marchuk
      Pages 1-5

  3. Adjoint Equations and Perturbation Theory

    1. Front Matter

      Pages 7-8
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    2. Main and Adjoint Equations. Perturbation Theory

      • Guri I. Marchuk
      Pages 9-94

    3. Simple Main and Adjoint Equations of Mathematical Physics

      • Guri I. Marchuk
      Pages 95-122

    4. Nonlinear Equations

      • Guri I. Marchuk
      Pages 123-162

    5. Inverse Problems and Adjoint Equations

      • Guri I. Marchuk
      Pages 163-205

  4. Problems of Environment and Optimization Methods on the Basis of Adjoint Equations

    1. Front Matter

      Pages 207-211
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    2. Analysis of Mathematical Models in Environmental Problems

      • Guri I. Marchuk
      Pages 212-268

    3. Adjoint Equations, Optimization

      • Guri I. Marchuk
      Pages 269-325

    4. Adjoint Equations and Models of General Circulation of Atmosphere and Ocean

      • Guri I. Marchuk
      Pages 326-388

    5. Adjoint Equations in Data Processing Problems

      • Guri I. Marchuk
      Pages 389-421

  5. Back Matter

    Pages 422-468
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Keywords

About this book

New statements of problems arose recently demanding thorough ana­ lysis. Notice, first of all, the statements of problems using adjoint equations which gradually became part of our life. Adjoint equations are capable to bring fresh ideas to various problems of new technology based on linear and nonlinear processes. They became part of golden fund of science through quantum mechanics, theory of nuclear reactors, optimal control, and finally helped in solving many problems on the basis of perturbation method and sensitivity theory. To emphasize the important role of adjoint problems in science one should mention four-dimensional analysis problem and solution of inverse problems. This range of problems includes first of all problems of global climate changes on our planet, state of environment and protection of environ­ ment against pollution, preservation of the biosphere in conditions of vigorous growth of population, intensive development of industry, and many others. All this required complex study of large systems: interac­ tion between the atmosphere and oceans and continents in the theory of climate, cenoses in the biosphere affected by pollution of natural and anthropogenic origin. Problems of local and global perturbations and models sensitivity to input data join into common complex system.

Authors and Affiliations

  • Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, Russia

    Guri I. Marchuk

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