Buch, Englisch, Band 62, 370 Seiten, Book w. online files / update, Format (B × H): 160 mm x 241 mm, Gewicht: 740 g
Reihe: Progress in Nonlinear Differential Equations and Their Applications
Buch, Englisch, Band 62, 370 Seiten, Book w. online files / update, Format (B × H): 160 mm x 241 mm, Gewicht: 740 g
Reihe: Progress in Nonlinear Differential Equations and Their Applications
ISBN: 978-0-8176-4302-7
Verlag: Birkhäuser Boston
This book examines a system of parabolic-elliptic partial differential eq- tions proposed in mathematical biology, statistical mechanics, and chemical kinetics. In the context of biology, this system of equations describes the chemotactic feature of cellular slime molds and also the capillary formation of blood vessels in angiogenesis. There are several methods to derive this system. One is the biased random walk of the individual, and another is the reinforced random walk of one particle modelled on the cellular automaton. In the context of statistical mechanics or chemical kinetics, this system of equations describes the motion of a mean ?eld of many particles, interacting under the gravitational inner force or the chemical reaction, and therefore this system is af?liated with a hierarchy of equations: Langevin, Fokker–Planck, Liouville–Gel’fand, and the gradient ?ow. All of the equations are subject to the second law of thermodynamics — the decrease of free energy. The mat- matical principle of this hierarchy, on the other hand, is referred to as the qu- tized blowup mechanism; the blowup solution of our system develops delta function singularities with the quantized mass.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
- Mathematik | Informatik EDV | Informatik Angewandte Informatik Computeranwendungen in Wissenschaft & Technologie
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
- Technische Wissenschaften Technik Allgemein Computeranwendungen in der Technik
- Naturwissenschaften Chemie Chemie Allgemein Chemometrik, Chemoinformatik
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
- Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
- Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
- Mathematik | Informatik EDV | Informatik Professionelle Anwendung Computer-Aided Design (CAD)
Weitere Infos & Material
Summary.- Background.- Fundamental Theorem.- Trudinger-Moser Inequality.- The Green’s Function.- Equilibrium States.- Blowup Analysis for Stationary Solutions.- Multiple Existence.- Dynamical Equivalence.- Formation of Collapses.- Finiteness of Blowup Points.- Concentration Lemma.- Weak Solution.- Hyperparabolicity.- Quantized Blowup Mechanism.- Theory of Dual Variation.
