000			03510nam a22004815i 4500
001			978-3-642-04631-5
003			DE-He213
005			20140220084527.0
007			cr nn 008mamaa
008			100301s2010 gw | s |||| 0|eng d
020			_a9783642046315 _9978-3-642-04631-5
024	7		_a10.1007/978-3-642-04631-5 _2doi
050		4	_aQA370-380
072		7	_aPBKJ _2bicssc
072		7	_aMAT007000 _2bisacsh
082	0	4	_a515.353 _223
100	1		_aYagi, Atsushi. _eauthor.
245	1	0	_aAbstract Parabolic Evolution Equations and their Applications _h[electronic resource] / _cby Atsushi Yagi.
264		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2010.
300			_bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aSpringer Monographs in Mathematics, _x1439-7382
505	0		_aPreliminaries -- Sectorial Operators -- Linear Evolution Equations -- Semilinear Evolution Equations -- Quasilinear Evolution Equations -- Dynamical Systems -- Numerical Analysis -- Semiconductor Models -- Activator–Inhibitor Models -- Belousov–Zhabotinskii Reaction Models -- Forest Kinematic Model -- Chemotaxis Models -- Termite Mound Building Model -- Adsorbate-Induced Phase Transition Model -- Lotka–Volterra Competition Model with Cross-Diffusion -- Characterization of Domains of Fractional Powers.
520			_aThe semigroup methods are known as a powerful tool for analyzing nonlinear diffusion equations and systems. The author has studied abstract parabolic evolution equations and their applications to nonlinear diffusion equations and systems for more than 30 years. He gives first, after reviewing the theory of analytic semigroups, an overview of the theories of linear, semilinear and quasilinear abstract parabolic evolution equations as well as general strategies for constructing dynamical systems, attractors and stable-unstable manifolds associated with those nonlinear evolution equations. In the second half of the book, he shows how to apply the abstract results to various models in the real world focusing on various self-organization models: semiconductor model, activator-inhibitor model, B-Z reaction model, forest kinematic model, chemotaxis model, termite mound building model, phase transition model, and Lotka-Volterra competition model. The process and techniques are explained concretely in order to analyze nonlinear diffusion models by using the methods of abstract evolution equations. Thus the present book fills the gaps of related titles that either treat only very theoretical examples of equations or introduce many interesting models from Biology and Ecology, but do not base analytical arguments upon rigorous mathematical theories.
650		0	_aMathematics.
650		0	_aDifferentiable dynamical systems.
650		0	_aDifferential equations, partial.
650		0	_aBiology _xMathematics.
650	1	4	_aMathematics.
650	2	4	_aPartial Differential Equations.
650	2	4	_aDynamical Systems and Ergodic Theory.
650	2	4	_aMathematical Biology in General.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783642046308
830		0	_aSpringer Monographs in Mathematics, _x1439-7382
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-642-04631-5
912			_aZDB-2-SMA
999			_c111622 _d111622