Mathematics for Industry

Non-Local Partial Differential Equations for Engineering and Biology

Mathematical Modeling and Analysis

Authors: Kavallaris, Nikos, Suzuki, Takashi

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  • Highlights practical use of non-local models considering any possible spatial dependence on the neighboring points as well as neglecting any feasible memory effects 
  • Supplies new mathematical methods for systems of PDE´s with examples of applications
  • Examines non-local models in MEMS technologies
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eBook $99.00
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  • ISBN 978-3-319-67944-0
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Hardcover $129.00
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Softcover $129.00
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About this book

This book presents new developments  in non-local mathematical modeling and mathematical analysis on the behavior of solutions with novel technical tools. Theoretical backgrounds in mechanics, thermo-dynamics, game theory, and theoretical biology are examined in details. It starts off with a review and summary of the basic ideas of mathematical modeling frequently used in the sciences and engineering. The authors then employ a number of models in bio-science and material science to demonstrate applications, and provide recent advanced studies, both on deterministic non-local partial differential equations and on some of their stochastic counterparts used in engineering. Mathematical models applied in engineering, chemistry, and biology are subject to conservation laws. For instance, decrease or increase in thermodynamic quantities and non-local partial differential equations, associated with the conserved physical quantities as parameters. These present novel mathematical objects are engaged with rich mathematical structures, in accordance with the interactions between species or individuals, self-organization, pattern formation, hysteresis. These models are based on various laws of physics, such as mechanics of continuum, electro-magnetic theory, and thermodynamics. This is why many areas of mathematics, calculus of variation, dynamical systems, integrable systems, blow-up analysis, and energy methods are indispensable in understanding and analyzing these phenomena.
This book aims for researchers and upper grade students in mathematics, engineering, physics, economics, and biology.

Reviews

“The book ends with an appendix that contains some non-local models of elastic string, point vortices, and geometric deformation. The models, mathematical concepts and proofs are clearly and rigorously presented, recommending the book to readers interested in non-locality and its mathematical analysis.” (Corina-Ștefania Drapaca, Mathematical Reviews, October, 2018)​

Table of contents (8 chapters)

Table of contents (8 chapters)

Buy this book

eBook $99.00
price for USA in USD
  • ISBN 978-3-319-67944-0
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • Immediate eBook download after purchase and usable on all devices
  • Bulk discounts available
Hardcover $129.00
price for USA in USD
Softcover $129.00
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Non-Local Partial Differential Equations for Engineering and Biology
Book Subtitle
Mathematical Modeling and Analysis
Authors
Series Title
Mathematics for Industry
Series Volume
31
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-67944-0
DOI
10.1007/978-3-319-67944-0
Hardcover ISBN
978-3-319-67942-6
Softcover ISBN
978-3-319-88515-5
Series ISSN
2198-350X
Edition Number
1
Number of Pages
XIX, 300
Number of Illustrations
16 b/w illustrations, 7 illustrations in colour
Topics