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Potential Method in Mathematical Theories of Multi-Porosity Media

  • Merab Svanadze
Book

Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 51)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Merab Svanadze
    Pages 1-23
  3. Merab Svanadze
    Pages 25-56
  4. Merab Svanadze
    Pages 83-96
  5. Merab Svanadze
    Pages 97-112
  6. Merab Svanadze
    Pages 113-130
  7. Merab Svanadze
    Pages 131-156
  8. Merab Svanadze
    Pages 157-166
  9. Merab Svanadze
    Pages 209-245
  10. Merab Svanadze
    Pages 247-271
  11. Merab Svanadze
    Pages 273-282
  12. Back Matter
    Pages 283-302

About this book

Introduction

This monograph explores the application of the potential method to three-dimensional problems of the mathematical theories of elasticity and thermoelasticity for multi-porosity materials.  These models offer several new possibilities for the study of important problems in engineering and mechanics involving multi-porosity materials, including geological materials (e.g., oil, gas, and geothermal reservoirs); manufactured porous materials (e.g., ceramics and pressed powders); and biomaterials (e.g., bone and the human brain).  

Proceeding from basic to more advanced material, the first part of the book begins with fundamental solutions in elasticity, followed by Galerkin-type solutions and Green’s formulae in elasticity and problems of steady vibrations, quasi-static, and pseudo-oscillations for multi-porosity materials.  The next part follows a similar format for thermoelasticity, concluding with a chapter on problems of heat conduction for rigid bodies. The final chapter then presents a number of open research problems to which the results presented here can be applied. All results discussed by the author have not been published previously and offer new insights into these models.

Potential Method in Mathematical Theories of Multi-Porosity Media will be a valuable resource for applied mathematicians, mechanical, civil, and aerospace engineers, and researchers studying continuum mechanics. Readers should be knowledgeable in classical theories of elasticity and thermoelasticity.

Keywords

Potential method book Potential method elasticity Porosity math Porosity materials Boundary Value Problems Multi-Porosity Media Galerkin-type solutions Laplace transform space Quadruple porosity materials Thermoelastic stress analysis Thermoelasticity theory Singular integral equation Potential Method Elasticity Mathematics and Solid Mechanics

Authors and affiliations

  • Merab Svanadze
    • 1
  1. 1.Ilia State UniversityTbilisiGeorgia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-28022-2
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-28021-5
  • Online ISBN 978-3-030-28022-2
  • Series Print ISSN 0939-6047
  • Series Online ISSN 2196-9973
  • Buy this book on publisher's site