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Non-local partial differential equat...

Kavallaris, Nikos I.

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

Record Type:	Electronic resources : Monograph/item
Title/Author:	Non-local partial differential equations for engineering and biology/ by Nikos I. Kavallaris, Takashi Suzuki.
Reminder of title:	mathematical modeling and analysis /
Author:	Kavallaris, Nikos I.
other author:	Suzuki, Takashi.
Published:	Cham :Springer International Publishing : : 2018.,
Description:	xix, 300 p. :ill., digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer eBooks
Subject:	Differential equations, Partial. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-67944-0
ISBN:	9783319679440

Non-local partial differential equations for engineering and biology = mathematical modeling and analysis /
Kavallaris, Nikos I.

Non-local partial differential equations for engineering and biologymathematical modeling and analysis /[electronic resource] :by Nikos I. Kavallaris, Takashi Suzuki. - Cham :Springer International Publishing :2018. - xix, 300 p. :ill., digital ;24 cm. - Mathematics for industry,v.312198-350X ;. - Mathematics for industry ;v.31..

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.

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.

ISBN: 9783319679440

Standard No.: 10.1007/978-3-319-67944-0doiSubjects--Topical Terms:

518115
Differential equations, Partial.

LC Class. No.: QA374

Dewey Class. No.: 515.353

Non-local partial differential equations for engineering and biology = mathematical modeling and analysis /
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245 1 0 $a Non-local partial differential equations for engineering and biology $h [electronic resource] : $b mathematical modeling and analysis / $c by Nikos I. Kavallaris, Takashi Suzuki.
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300 $a xix, 300 p. : $b ill., digital ; $c 24 cm.
490 1 $a Mathematics for industry, $x 2198-350X ; $v v.31
505 0 $a 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.
520 $a 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.
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