Non-Local Partial Differential Equations for Engineering and Biology

Mathematical Modeling and Analysis

  • Nikos I. Kavallaris
  • Takashi Suzuki

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

Table of contents

  1. Front Matter
    Pages i-xix
  2. Applications in Engineering

    1. Front Matter
      Pages 1-1
    2. Nikos I. Kavallaris, Takashi Suzuki
      Pages 3-63
    3. Nikos I. Kavallaris, Takashi Suzuki
      Pages 65-108
    4. Nikos I. Kavallaris, Takashi Suzuki
      Pages 109-129
    5. Nikos I. Kavallaris, Takashi Suzuki
      Pages 131-159
  3. Emotion in Music

    1. Front Matter
      Pages 161-161
    2. Nikos I. Kavallaris, Takashi Suzuki
      Pages 163-193
    3. Nikos I. Kavallaris, Takashi Suzuki
      Pages 195-227
    4. Nikos I. Kavallaris, Takashi Suzuki
      Pages 229-249
    5. Nikos I. Kavallaris, Takashi Suzuki
      Pages 251-290
  4. Back Matter
    Pages 291-300

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.


Applications of Loktka- Volterra Models Bio-science Modelling Blow up analysis for non-local diffusion Deterministic non-local PDE´s Models Non-local PDE's Nonlocal equations

Authors and affiliations

  • Nikos I. Kavallaris
    • 1
  • Takashi Suzuki
    • 2
  1. 1.Department of MathematicsUniversity of ChesterChesterUnited Kingdom
  2. 2.Department of MathematicsOsaka UniversityOsakaJapan

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Engineering Engineering (R0)
  • Print ISBN 978-3-319-67942-6
  • Online ISBN 978-3-319-67944-0
  • Series Print ISSN 2198-350X
  • Series Online ISSN 2198-3518
  • Buy this book on publisher's site