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Advances in Mechanics and Mathematics

Mathematical Aspects of Multi–Porosity Continua

Authors: Straughan, Brian

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  • Presents new analyses of nonlinear waves
  • Examples provided at the end of every chapter
  • Provides new models, including second sound
  • Includes an extensive bibliography
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eBook 47,59 €
price for Spain (gross)
  • ISBN 978-3-319-70172-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
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  • Immediate eBook download after purchase
Hardcover 59,27 €
price for Spain (gross)
  • ISBN 978-3-319-70171-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 59,27 €
price for Spain (gross)
  • ISBN 978-3-319-88895-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this Textbook

This book is devoted to describing theories for porous media where such pores have an inbuilt macro structure and a micro structure. For example, a double porosity material has pores on a macro scale, but additionally there are cracks or fissures in the solid skeleton. The actual body is allowed to deform and thus the underlying theory is one of elasticity. Various different descriptions are reviewed.

Chapter 1 introduces the classical linear theory of elastodynamics together with uniqueness and continuous dependence results. Chapters 2 and 3 review developments of theories for double and triple porosity using a pressure-displacement structure and also using voids-displacement. Chapter 4 compares various aspects of the pressure-displacement and voids-displacement theories via uniqueness studies and wave motion analysis. Mathematical analyses of double and triple porosity materials are included concentrating on uniqueness and stability studies in chapters 5 to 7. In chapters 8 and 9 the emphasis is on wave motion in double porosity materials with special attention paid to nonlinear waves. The final chapter embraces a novel area where an elastic body with a double porosity structure is analyzed, but the thermodynamics allows for heat to travel as a wave rather than simply by diffusion.

This book will be of value to mathematicians, theoretical engineers and other practitioners who are interested in double or triple porosity elasticity and its relevance to many diverse applications.

About the authors

Brian Straughan is a Professor in the Department of Mathematical Sciences at Durham University in Durham, UK.  He is a member of the Center for the Coevolution of Biology and Culture, and his research interests include: computational mathematics, partial differential equations, and stability.

Reviews

“This book contains a review and new elements concerning the porous media with double and triple porosity. … Each chapter contains a large number of exercises, very useful for students and researchers. The book is very useful to those interested in porous media and new materials technology.” (Gelu Paşa, zbMATH 1390.74009, 2018)

Table of contents (10 chapters)

Table of contents (10 chapters)

Buy this book

eBook 47,59 €
price for Spain (gross)
  • ISBN 978-3-319-70172-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 59,27 €
price for Spain (gross)
  • ISBN 978-3-319-70171-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 59,27 €
price for Spain (gross)
  • ISBN 978-3-319-88895-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Mathematical Aspects of Multi–Porosity Continua
Authors
Series Title
Advances in Mechanics and Mathematics
Series Volume
38
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-70172-1
DOI
10.1007/978-3-319-70172-1
Hardcover ISBN
978-3-319-70171-4
Softcover ISBN
978-3-319-88895-8
Series ISSN
1571-8689
Edition Number
1
Number of Pages
IX, 208
Number of Illustrations
3 b/w illustrations, 4 illustrations in colour
Topics