With the unifying theme of abstract evolutionary equations, both linear and nonlinear, in a complex environment, the book presents a multidisciplinary blend of topics, spanning the fields of theoretical and applied functional analysis, partial differential equations, probability theory and numerical analysis applied to various models coming from theoretical physics, biology, engineering and complexity theory.
Truly unique features of the book are: the first simultaneous presentation of two complementary approaches to fragmentation and coagulation problems, by weak compactness methods and by using semigroup techniques, comprehensive exposition of probabilistic methods of analysis of long term dynamics of dynamical systems, semigroup analysis of biological problems and cutting edge pattern formation theory.
The book will appeal to postgraduate students and researchers specializing in applications of mathematics to problems arising in natural sciences and engineering.
Author(s): Jacek Banasiak, Mustapha Mokhtar-Kharroubi (eds.)
Series: Lecture Notes in Mathematics 2126
Edition: 1
Publisher: Springer International Publishing
Year: 2015
Language: English
Pages: 493
Tags: Partial Differential Equations; Mathematical and Computational Biology; Mathematical Physics; Graph Theory; Dynamical Systems and Ergodic Theory; Operator Theory
Front Matter....Pages i-xi
Applying Functional Analytic Techniques to Evolution Equations....Pages 1-46
Boundary Conditions in Evolutionary Equations in Biology....Pages 47-92
Introduction to Complex Networks: Structure and Dynamics....Pages 93-131
Kinetic Models in Natural Sciences....Pages 133-198
Weak Compactness Techniques and Coagulation Equations....Pages 199-253
Stochastic Operators and Semigroups and Their Applications in Physics and Biology....Pages 255-318
Spectral Theory for Neutron Transport....Pages 319-386
Reaction-Diffusion-ODE Models of Pattern Formation....Pages 387-438
Nonlinear Hyperbolic Systems of Conservation Laws and Related Applications....Pages 439-493
Back Matter....Pages 495-496
