Springer Monographs in Mathematics

Nonlinear PDEs

Mathematical Models in Biology, Chemistry and Population Genetics

Authors: Ghergu, Marius, Radulescu, Vicentiu

  • Foreword by Viorel Barbu
  • Methods developed can be applied to large classes of models arising in applications
  • Interdisciplinary dialogue between mathematics, biology, chemistry and population genetics​
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  • ISBN 978-3-642-22664-9
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Hardcover $124.00
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  • ISBN 978-3-642-22663-2
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Softcover $124.00
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  • ISBN 978-3-642-26984-4
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About this book

The emphasis throughout the present volume is on the practical application of theoretical mathematical models helping to unravel the underlying mechanisms involved in processes from mathematical physics and biosciences. It has been conceived as a unique collection of abstract methods dealing especially with nonlinear partial differential equations (either stationary or evolutionary) that are applied to understand concrete processes involving some important applications related to phenomena such as: boundary layer phenomena for viscous fluids, population dynamics,, dead core phenomena, etc. It addresses researchers and post-graduate students working at the interplay between mathematics and other fields of science and technology and is a comprehensive introduction to the theory of nonlinear partial differential equations  and its main principles also presents their real-life applications in various contexts: mathematical physics, chemistry, mathematical biology, and population genetics. Based on the authors' original work, this volume provides an overview of the field, with examples suitable for researchers but also for graduate students entering research. The method of presentation appeals to readers with diverse backgrounds in partial differential equations and functional analysis. Each chapter includes detailed heuristic arguments, providing thorough motivation for the material developed later in the text. The content demonstrates in a firm way that partial differential equations can be used to address a large variety of phenomena occurring in and influencing our daily lives. The extensive reference list and index make this book a valuable resource for researchers working in a variety of fields and who are interested in phenomena modeled by nonlinear partial differential equations.​

Reviews

From the reviews:

“This is a unique treatise on the application of advanced nonlinear operator theory. … The importance of mathematics in biosciences is very well supported by a great number of detailed examples in the text. The book can used for advanced graduate courses as well as a reference for advanced researchers in applied sciences. The authors have accomplished a wonderful mathematical journey.” (Dhruba Adhikari, MAA Reviews, January, 2013)

“The purpose of this book is to introduce fundamental techniques that are used for modeling and mathematical analysis of problems arising in chemistry, biology or genetics. … The book concludes with the extensive bibliography (217 references) and a detailed index. It will be useful for researchers, graduate students and specialists working with partial differential equations and their applications in chemistry and biomathematics.” (Yuri V. Rogovchenko, Zentralblatt MATH, Vol. 1227, 2012)


Table of contents (10 chapters)

  • Overview of Mathematical Methods in Partial Differential Equations

    Ghergu, Marius (et al.)

    Pages 1-18

  • Liouville Type Theorems for Elliptic Operators in Divergence Form

    Ghergu, Marius (et al.)

    Pages 19-27

  • Blow-Up Boundary Solutions of the Logistic Equation

    Ghergu, Marius (et al.)

    Pages 29-115

  • Singular Lane–Emden–Fowler Equations and Systems

    Ghergu, Marius (et al.)

    Pages 117-165

  • Singular Elliptic Inequalities in Exterior Domains

    Ghergu, Marius (et al.)

    Pages 167-210

Buy this book

eBook $89.00
price for USA (gross)
  • ISBN 978-3-642-22664-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $124.00
price for USA
  • ISBN 978-3-642-22663-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $124.00
price for USA
  • ISBN 978-3-642-26984-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Nonlinear PDEs
Book Subtitle
Mathematical Models in Biology, Chemistry and Population Genetics
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2012
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-22664-9
DOI
10.1007/978-3-642-22664-9
Hardcover ISBN
978-3-642-22663-2
Softcover ISBN
978-3-642-26984-4
Series ISSN
1439-7382
Edition Number
1
Number of Pages
XVIII, 394
Topics