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Nonlinear PDEs

Mathematical Models in Biology, Chemistry and Population Genetics

  • Book
  • © 2012

Overview

Authors:
  1. Marius Ghergu

    1. School of Mathematical Sciences, University College Dublin, Dublin 4, Ireland

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  2. Vicenţiu D. Rӑdulescu

    1. Simion Stoilow Mathematics Institute, Romanian Academy, Bucharest, Romania

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    You can also search for this author in PubMed   Google Scholar

  • 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?
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer Monographs in Mathematics (SMM)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xviii
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  2. Overview of Mathematical Methods in Partial Differential Equations

    • Marius Ghergu, Vicenţiu D. Rǎdulescu
    Pages 1-18

  3. Liouville Type Theorems for Elliptic Operators in Divergence Form

    • Marius Ghergu, Vicenţiu D. Rǎdulescu
    Pages 19-27

  4. Blow-Up Boundary Solutions of the Logistic Equation

    • Marius Ghergu, Vicenţiu D. Rǎdulescu
    Pages 29-115

  5. Singular Lane–Emden–Fowler Equations and Systems

    • Marius Ghergu, Vicenţiu D. Rǎdulescu
    Pages 117-165

  6. Singular Elliptic Inequalities in Exterior Domains

    • Marius Ghergu, Vicenţiu D. Rǎdulescu
    Pages 167-210

  7. Two Quasilinear Elliptic Problems

    • Marius Ghergu, Vicenţiu D. Rǎdulescu
    Pages 211-243

  8. Some Classes of Polyharmonic Problems

    • Marius Ghergu, Vicenţiu D. Rǎdulescu
    Pages 245-266

  9. Large Time Behavior of Solutions for Degenerate Parabolic Equations

    • Marius Ghergu, Vicenţiu D. Rǎdulescu
    Pages 267-286

  10. Reaction-Diffusion Systems Arising in Chemistry

    • Marius Ghergu, Vicenţiu D. Rǎdulescu
    Pages 287-335

  11. Pattern Formation and the Gierer–Meinhardt Model in Molecular Biology

    • Marius Ghergu, Vicenţiu D. Rǎdulescu
    Pages 337-367

  12. Back Matter

    Pages 369-391
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Keywords

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)

Authors and Affiliations

  • School of Mathematical Sciences, University College Dublin, Dublin 4, Ireland

    Marius Ghergu

  • Simion Stoilow Mathematics Institute, Romanian Academy, Bucharest, Romania

    Vicenţiu D. Rӑdulescu

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