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Non-Local Partial Differential Equations for Engineering and Biology

Mathematical Modeling and Analysis

  • Book
  • © 2018

Overview

Authors:
  1. Nikos I. Kavallaris

    1. Department of Mathematics, University of Chester, Chester, United Kingdom

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    You can also search for this author in PubMed   Google Scholar

  2. Takashi Suzuki

    1. Department of Mathematics, Osaka University, Osaka, Japan

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    You can also search for this author in PubMed   Google Scholar

  • 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
  • Includes supplementary material: sn.pub/extras

Part of the book series: Mathematics for Industry (MFI, volume 31)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xix
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  2. Applications in Engineering

    1. Front Matter

      Pages 1-1
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    2. Micro-Electro-Mechanical-Systems (MEMS)

      • Nikos I. Kavallaris, Takashi Suzuki
      Pages 3-63

    3. Ohmic Heating Phenomena

      • Nikos I. Kavallaris, Takashi Suzuki
      Pages 65-108

    4. Linear Friction Welding

      • Nikos I. Kavallaris, Takashi Suzuki
      Pages 109-129

    5. Resistance Spot Welding

      • Nikos I. Kavallaris, Takashi Suzuki
      Pages 131-159

  3. Emotion in Music

    1. Front Matter

      Pages 161-161
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    2. Gierer–Meinhardt System

      • Nikos I. Kavallaris, Takashi Suzuki
      Pages 163-193

    3. A Non-local Model Illustrating Replicator Dynamics

      • Nikos I. Kavallaris, Takashi Suzuki
      Pages 195-227

    4. A Non-local Model Arising in Chemotaxis

      • Nikos I. Kavallaris, Takashi Suzuki
      Pages 229-249

    5. A Non-local Reaction-Diffusion System Illustrating Cell Dynamics

      • Nikos I. Kavallaris, Takashi Suzuki
      Pages 251-290

  4. Back Matter

    Pages 291-300
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Keywords

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 objectsare 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

“Overall the book is concerned with highly specific applications of non-local PDEs. This is a very advanced book which will be of interest to people who have specific interests in one or more topics covered by the book." (John Bartlett, Mathematics Today, Vol. 56 (5), October, 2020)




“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)​

Authors and Affiliations

  • Department of Mathematics, University of Chester, Chester, United Kingdom

    Nikos I. Kavallaris

  • Department of Mathematics, Osaka University, Osaka, Japan

    Takashi Suzuki

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