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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
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.
Content Level »Research
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