Evolution Equations Arising in the Modelling of Life Sciences
By: by Messoud Efendiev
Contributors: SpringerLink (Online service)
Series: International Series of Numerical Mathematics -- 163
Publisher: Springer Basel; Imprint: Birkhäuser
Published: 2013
Place of publication: Basel
Language: eng
Format: [electronic resource] /
Number of pages: 217
ISBN-13: 9783034806152
Subjects: Ecology; Biological models; Mathematical and Computational Biology; Partial Differential equations; Cellular and Medical Topics Physiological; Theoretical Ecology/Statistics; Systems biology; Mathematics; Physiology
Description: 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.
Table of contents: title: Preface; title: 1 Auxiliary Materials; title: 2 Global attractors for autonomous evolution equations; title: 3 Verifying life science models containing diffusion, transport and interaction of species; title: 4 Positivity criterion for systems of stochastic PDEs; title: Existence and longtime behaviour of a biofilm model; title: 6 The blood coagulation cascade in a perfusion experiment: example from pharmaceutical industry; title: Index.​.