Evolution Equations Arising in the Modelling of Life Sciences

1. Front Matter

   Pages I-XII

   PDF

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

   PDF

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.

• 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
• partial differential equations
• Systems Biology

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)

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

  Messoud Efendiev

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

Policies and ethics