TY  - BOOK
AU  - Suzuki,Takashi
ED  - SpringerLink (Online service)
TI  - Free Energy and Self-Interacting Particles
T2  - Progress in Nonlinear Differential Equations and Their Applications
SN  - 9780817644369
U1  - 515.353 23
PY  - 2005///
CY  - Boston, MA
PB  - Birkhäuser Boston
KW  - MATHEMATICS
KW  - CHEMISTRY
KW  - DIFFERENTIAL EQUATIONS, PARTIAL
KW  - BIOLOGY
KW  - MATHEMATICAL PHYSICS
KW  - ENGINEERING MATHEMATICS
KW  - PARTIAL DIFFERENTIAL EQUATIONS
KW  - APPLICATIONS OF MATHEMATICS
KW  - MATHEMATICAL METHODS IN PHYSICS
KW  - MATHEMATICAL BIOLOGY IN GENERAL
KW  - APPL.MATHEMATICS/COMPUTATIONAL METHODS OF ENGINEERING
KW  - MATH. APPLICATIONS IN CHEMISTRY
N1  - 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
N2  - This book examines a nonlinear system of parabolic partial differential equations (PDEs) arising in mathematical biology and statistical mechanics. In the context of biology, the system typically describes the chemotactic feature of cellular slime molds. One way of deriving these equations is via the random motion of a particle in a cellular automaton. In statistical mechanics the system is associated with the motion of the mean field of self-interacting particles under gravitational force. Physically, such a system is related to Langevin, Fokker-Planck, Liouville and gradient flow equations. Mathematically, the mechanism can be referred to as a quantized blowup. This book describes the whole picture, i.e., the mathematical and physical principles: derivation of a series of equations, biological modeling based on biased random walks, the study of equilibrium states via the variational structure derived from the free energy, and the quantized blowup mechanism based on several PDE techniques
UR  - http://dx.doi.org/10.1007/0-8176-4436-9
ER  -