Non-local partial differential equations for engineering and biology : mathematical modeling and analysis

Author(s)

Bibliographic Information

Non-local partial differential equations for engineering and biology : mathematical modeling and analysis

Nikos I. Kavallaris, Takashi Suzuki

(Mathematics for industry / editor in chief, Masato Wakayama, v. 31)

Springer, c2018

Available at  / 2 libraries

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Note

Includes bibliographical references and index

Description and Table of Contents

Description

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.

Table of Contents

Dedication.- Preface.- Acknowledgements.- Part I Applications in Engineering.- Micro-electro-mechanical-systems(MEMS).- Ohmic Heating Phenomena.- Linear Friction Welding.- Resistance Spot Welding.- Part II Applications in Biology.- Gierer-Meinhardt System.- A Non-local Model Illustrating Replicator Dynamics.- A Non-local Model Arising in Chemotaxis.- A Non-local Reaction-Diffusion System Illustrating Cell Dynamics.- Appendices.- Index.

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Details

  • NCID
    BB25755708
  • ISBN
    • 9783319679426
  • LCCN
    2017957187
  • Country Code
    sz
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Cham
  • Pages/Volumes
    xix, 300 p.
  • Size
    25 cm
  • Parent Bibliography ID
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