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Evolution Equations Arising in the Modelling of Life Sciences

  • Messoud Efendiev

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

Table of contents

About this book

Introduction

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.

Keywords

biofilm model blood coagulation cascade in a perfusion experiment diffusion, transport and interaction of species global attractors for autonomous evolution equations nonlinear reaction-diffusion convective equations systems of stochastic PDEs

Authors and affiliations

  • Messoud Efendiev
    • 1
  1. 1.Institute of Biomathematics and BiometryHelmholtz Center MunichNeuherbergGermany

Bibliographic information

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