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Evolution Equations Arising in the Modelling of Life Sciences

  • Book
  • © 2013

Overview

Authors:
  1. Messoud Efendiev

    1. Institute of Biomathematics and Biometry, Helmholtz Center Munich, Neuherberg, Germany

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

Part of the book series: International Series of Numerical Mathematics (ISNM, volume 163)

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Table of contents (6 chapters)

  1. Front Matter

    Pages I-XII
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  2. Auxiliary Materials

    • Messoud Efendiev
    Pages 1-15

  3. Global Attractors for Autonomous Evolution Equations

    • Messoud Efendiev
    Pages 17-23

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

    • Messoud Efendiev
    Pages 25-57

  5. Positivity Criterion for Systems of Stochastic PDEs

    • Messoud Efendiev
    Pages 59-85

  6. Existence and Longtime Behaviour of a Biofilm Model

    • Messoud Efendiev
    Pages 87-194

  7. The Blood Coagulation Cascade in a Perfusion Experiment: Example from the Pharmaceutical Industry

    • Messoud Efendiev
    Pages 195-207

  8. Back Matter

    Pages 209-217
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Keywords

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.

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)

Authors and Affiliations

  • Institute of Biomathematics and Biometry, Helmholtz Center Munich, Neuherberg, Germany

    Messoud Efendiev

About the author

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

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