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Higher Order Partial Differential Equations in Clifford Analysis

Effective Solutions to Problems

  • Book
  • © 2003

Overview

Authors:
  1. Elena Obolashvili

    1. Georgian Academy of Sciences, A. Razmadze Mathematical Institute, Tbilisi, Georgia

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  • New types of parabolic equations of high order considered in the Clifford analysis framework
  • Pluri-Beltrami and plurigeneralized Beltrami equations for ellpitic and hyperbolic cases
  • Boundary and initial value problems solved in quadratures

Part of the book series: Progress in Mathematical Physics (PMP, volume 28)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-viii
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  2. Boundary Value Problems for Regular, Generalized Regular and Pluriregular Elliptic Equations

    1. Front Matter

      Pages 1-1
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    2. Two-Dimensional Cases

      • Elena Obolashvili
      Pages 3-66

    3. Multidimensional Cases

      • Elena Obolashvili
      Pages 67-122

  3. Initial Value Problems for Regular and Pluriregular, Hyperbolic and Parabolic Equations

    1. Front Matter

      Pages 123-123
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    2. Hyperbolic and Plurihyperbolic Equations in Clifford Analysis

      • Elena Obolashvili
      Pages 125-150

    3. Parabolic and Pluriparabolic Equations in Clifford Analysis

      • Elena Obolashvili
      Pages 151-169

  4. Epilogue

    1. Epilogue

      • Elena Obolashvili
      Pages 171-171

  5. Back Matter

    Pages 173-178
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Keywords

About this book

The most important thing is to write equations in a beautiful form and their success in applications is ensured. Paul Dirac The uniqueness and existence theorems for the solutions of boundary and initial value problems for systems of high-order partial differential equations (PDE) are sufficiently well known. In this book, the problems considered are those whose solutions can be represented in quadratures, i.e., in an effective form. Such problems have remarkable applications in mathematical physics, the mechanics of deformable bodies, electro­ magnetism, relativistic quantum mechanics, and some of their natural generalizations. Almost all such problems can be set in the context of Clifford analysis. Moreover, they can be obtained without applying any physical laws, a circumstance that gives rise to the idea that Clifford analysis itself can suggest generalizations of classical equations or new equations altogether that may have some physical content. For that reason, Clifford analysis represents one of the most remarkable fields in modem mathematics as well as in modem physics.

Authors and Affiliations

  • Georgian Academy of Sciences, A. Razmadze Mathematical Institute, Tbilisi, Georgia

    Elena Obolashvili

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