Mustapha Mokhtar-Kharroubi - Böcker

This monograph provides new functional analytic developments on spectral problems in various applied fields such as jump equations, Kolmogorov differential equations, weighted graphs, neutron transport theory, population dynamics, linearized non-local Allen–Cahn equations and perturbed convolution semigroups.  With an emphasis on spectral problems (in Lebesgue spaces) connected to positivity, it uses powerful tools developed over the last two decades to unify and extend established results in various directions, offering new perspectives in a diverse range of subjects.  Many open questions are scattered throughout, in the hope of promoting further research. Covering topics lying at the intersection between functional analysis and partial differential equations, the book is primarily targeted toward applied mathematicians working in kinetic theory, probability theory, mathematical biology and, more generally, partial differential equations, who are interested in peripheral spectral theory. It may also draw pure mathematicians working in semigroup theory towards very rich applied areas. Although mainly aimed at professional mathematicians, it will also be useful to PhD students and post-doctoral researchers.  The long chapter devoted to transport theory will be of interest to physicists or engineers involved in neutron transport.

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.