Non-Local Partial Differential Equations for Engineering and Biology

Mathematical Modeling and Analysis

Nikos I. Kavallaris, Takashi Suzuki (Autoren)

Buch | Hardcover

XIX, 300 Seiten

2017 | 1st ed. 2018
Springer International Publishing (Verlag)
978-3-319-67942-6 (ISBN)

Artikel merken

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.

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.

"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- tefania Drapaca, Mathematical Reviews, October, 2018)

Erscheinungsdatum	25.12.2017
Reihe/Serie	Mathematics for Industry
Zusatzinfo	XIX, 300 p. 23 illus., 7 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	659 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Themenwelt	Technik ► Maschinenbau
Schlagworte	Applications of Loktka- Volterra Models • Biology, life sciences • Bio-science Modelling • Blow up analysis for non-local diffusion • Computer Appl. in Life Sciences • Deterministic non-local PDE s • Deterministic non-local PDE´s • Differential calculus & equations • Differential calculus & equations • Engineering • Engineering: general • industrial chemistry & chemical engineering • Industrial chemistry & chemical engineering • Industrial Chemistry/Chemical Engineering • Information technology: general issues • Mathematical Applications in the Physical Sciences • Mathematical Modelling • mechanics of solids • Models • Nonlocal equations • Non-local PDE's • Partial differential equations • Theoretical and Applied Mechanics
ISBN-10	3-319-67942-2 / 3319679422
ISBN-13	978-3-319-67942-6 / 9783319679426
Zustand	Neuware