Free Energy and Self-Interacting Particles

• Corporate Author: SpringerLink (Online service)
• Other Authors: Suzuki, Takashi (Editor)
• Format: Electronic eBook
• Language: English
• Published: Boston, MA : Birkhäuser Boston, 2005.
• Series: Progress in Nonlinear Differential Equations and Their Applications ; 62
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Partial differential equations.; Applied mathematics.; Engineering mathematics.; Biomathematics.; Physics.; Applications of Mathematics.; Partial Differential Equations.; Analysis.; Mathematical Methods in Physics.; Mathematical and Computational Biology.; Appl.Mathematics/Computational Methods of Engineering.

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 format...

Table of Contents:

• 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.