Evolution Equations Arising in the Modelling of Life Sciences

by Messoud Efendiev

Overview

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.

Product Details

ISBN-13:	9783034806145
Publisher:	Springer Basel
Publication date:	03/06/2013
Series:	International Series of Numerical Mathematics , #163
Edition description:	2013
Pages:	217
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

About the Author

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

Table of Contents

Preface.- 1 Auxiliary Materials.- 2 Global attractors for autonomous evolution equations.- 3 Verifying life science models containing diffusion, transport and interaction of species.- 4 Positivity criterion for systems of shastic PDEs.- Existence and longtime behaviour of a biofilm model.- 6 The blood coagulation cascade in a perfusion experiment: example from pharmaceutical industry.- Index.​

Editorial 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)

From the Publisher