Multiscale Problems in the Life Sciences: From Microscopic to Macroscopic

✍ Scribed by Jacek Banasiak, Mark A. J. Chaplain, Jacek Miękisz (auth.), Vincenzo Capasso, Mirosław Lachowicz (eds.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2008
• Tongue: English
• Leaves: 340
• Series: Lecture Notes in Mathematics 1940
• Edition: 1
• Category: Library

✦ Synopsis

The aim of this volume that presents Lectures given at a joint CIME and Banach Center Summer School, is to offer a broad presentation of a class of updated methods providing a mathematical framework for the development of a hierarchy of models of complex systems in the natural sciences, with a special attention to Biology and Medicine. Mastering complexity implies sharing different tools requiring much higher level of communication between different mathematical and scientific schools, for solving classes of problems of the same nature. Today more than ever, one of the most important challenges derives from the need to bridge parts of a system evolving at different time and space scales, especially with respect to computational affordability. As a result the content has a rather general character; the main role is played by stochastic processes, positive semigroups, asymptotic analysis, kinetic theory, continuum theory and game theory.

✦ Table of Contents

Front Matter....Pages i-xii
Positivity in Natural Sciences....Pages 1-89
Rescaling Stochastic Processes: Asymptotics....Pages 91-146
Modelling Aspects of Cancer Growth: Insight from Mathematical and Numerical Analysis and Computational Simulation....Pages 147-200
Lins Between Microscopic and Macroscopic Descriptions....Pages 201-267
Evolutionary Game Theory and Population Dynamics....Pages 269-316
Erratum....Pages 323-323
Back Matter....Pages 317-321

✦ Subjects

Partial Differential Equations; Operator Theory; Probability Theory and Stochastic Processes; Game Theory, Economics, Social and Behav. Sciences