Free energy and self-interacting particles

Description

Examines a nonlinear system of parabolic partial differential equations (PDE) arising in mathematical biology and statistical mechanics. This book describes the mathematical and physical principles: derivation of a series of equations, biological modeling based on biased random walks, and quantized blowup mechanism based on several PDE techniques. Abstract: Examines a nonlinear system of parabolic partial differential equations (PDE) arising in mathematical biology and statistical mechanics. This book describes the mathematical and physical principles: derivation of a series of equations, biological modeling based on biased random walks, and quantized blowup mechanism based on several PDE techniques Content: Front Matter 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 Back Matter.