Free Energy and Self-Interacting Particles / edited by Takashi Suzuki
(Progress in Nonlinear Differential Equations and Their Applications ; 62)
| データ種別 | 電子ブック |
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| 出版情報 | Boston, MA : Birkhäuser Boston , 2005 |
| 本文言語 | 英語 |
| 大きさ | XIII, 370 p : online resource |
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| 内容注記 | 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 |
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| 一般注記 | 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 |
| 著者標目 | Suzuki, Takashi editor SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Mathematical analysis LCSH:Analysis (Mathematics) LCSH:Partial differential equations LCSH:Applied mathematics LCSH:Engineering mathematics LCSH:Biomathematics LCSH:Physics FREE:Mathematics FREE:Applications of Mathematics FREE:Partial Differential Equations FREE:Analysis FREE:Mathematical Methods in Physics FREE:Mathematical and Computational Biology FREE:Appl.Mathematics/Computational Methods of Engineering |
| 分 類 | DC23:519 |
| 巻冊次 | ISBN:9780817644369 
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| ISBN | 9780817644369 |
| URL | http://dx.doi.org/10.1007/0-8176-4436-9 |
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