International Series of Numerical Mathematics

Evolution Equations Arising in the Modelling of Life Sciences

Authors: Efendiev, Messoud

  • Deals with a new class of nonlinear reaction-diffusion convective equations simultaneously comprising two kinds of degeneracy
  • Derives and analyses realistic life science models based on experimental data  
  • Represents a good example of the usefulness of interdisciplinary research
  • Adresses researchers in biomathematics as well as (post-)graduate students interested in applications of new mathematical methods in the life sciences ​
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About this book

This book deals with the modeling, analysis and simulation of problems arising in the life sciences, and especially in biological processes. The models and findings presented result from intensive discussions with microbiologists, doctors and medical staff, physicists, chemists and industrial engineers and are based on experimental data. They lead to a new class of degenerate density-dependent nonlinear reaction-diffusion convective equations that simultaneously comprise two kinds of degeneracy: porous-medium and fast-diffusion type degeneracy. To date, this class is still not clearly understood in the mathematical literature and thus especially interesting. The author both derives realistic life science models and their above-mentioned governing equations of the degenerate types and systematically studies these classes of equations. In each concrete case well-posedness, the dependence of solutions on boundary conditions reflecting some properties of the environment, and the large-time behavior of solutions are investigated and in some instances also studied numerically.

About the authors

Messoud Efendiev is professor of mathematics, especially dynamical system, at the Helmholtz Center Munich, Germany.

Reviews

From the reviews:

 

“The general aim of this book is to derive and treat partial differential equations of reaction-diffusion-convection type with degeneracies modelling some problems in the life sciences. … a valuable source of reference for researchers using partial differential equations for modelling biological processes. Postgraduate students with an appropriate background … may also find several chapters of the book useful.” (József Zoltán Farkas, Mathematical Reviews, February, 2014)

Table of contents (6 chapters)

  • Auxiliary Materials

    Efendiev, Messoud

    Pages 1-15

  • Global Attractors for Autonomous Evolution Equations

    Efendiev, Messoud

    Pages 17-23

  • Verifying Life Science Models Containing Diffusion, Transport and Interaction of Species

    Efendiev, Messoud

    Pages 25-57

  • Positivity Criterion for Systems of Stochastic PDEs

    Efendiev, Messoud

    Pages 59-85

  • Existence and Longtime Behaviour of a Biofilm Model

    Efendiev, Messoud

    Pages 87-194

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-3-0348-0615-2
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-3-0348-0614-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA
  • ISBN 978-3-0348-0780-7
  • 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
Evolution Equations Arising in the Modelling of Life Sciences
Authors
Series Title
International Series of Numerical Mathematics
Series Volume
163
Copyright
2013
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel
eBook ISBN
978-3-0348-0615-2
DOI
10.1007/978-3-0348-0615-2
Hardcover ISBN
978-3-0348-0614-5
Softcover ISBN
978-3-0348-0780-7
Series ISSN
0373-3149
Edition Number
1
Number of Pages
XII, 217
Topics