000			03300nam a22005295i 4500
001			978-0-8176-4436-9
003			DE-He213
005			20251006084434.0
007			cr nn 008mamaa
008			100301s2005 xxu| s |||| 0|eng d
020			_a9780817644369
020			_a99780817644369
024	7		_a10.1007/0-8176-4436-9 _2doi
082	0	4	_a515.353 _223
100	1		_aSuzuki, Takashi. _eeditor.
245	1	0	_aFree Energy and Self-Interacting Particles _h[electronic resource] / _cedited by Takashi Suzuki.
264		1	_aBoston, MA : _bBirkhäuser Boston, _c2005.
300			_aXIII, 366 p. 7 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aProgress in Nonlinear Differential Equations and Their Applications ; _v62
505	0		_aSummary -- 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.
520			_aThis 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.
650		0	_aMATHEMATICS.
650		0	_aCHEMISTRY _xMATHEMATICS.
650		0	_aDIFFERENTIAL EQUATIONS, PARTIAL.
650		0	_aBIOLOGY _xMATHEMATICS.
650		0	_aMATHEMATICAL PHYSICS.
650		0	_aENGINEERING MATHEMATICS.
650	1	4	_aMATHEMATICS.
650	2	4	_aPARTIAL DIFFERENTIAL EQUATIONS.
650	2	4	_aAPPLICATIONS OF MATHEMATICS.
650	2	4	_aMATHEMATICAL METHODS IN PHYSICS.
650	2	4	_aMATHEMATICAL BIOLOGY IN GENERAL.
650	2	4	_aAPPL.MATHEMATICS/COMPUTATIONAL METHODS OF ENGINEERING.
650	2	4	_aMATH. APPLICATIONS IN CHEMISTRY.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780817643027
830		0	_aProgress in Nonlinear Differential Equations and Their Applications ; _v62
856	4	0	_uhttp://dx.doi.org/10.1007/0-8176-4436-9 _zVer el texto completo en las instalaciones del CICY
912			_aZDB-2-SMA
942			_2ddc _cER
999			_c59635 _d59635