000			02986nam a22004933i 4500
001			EBC3114483
003			MiAaPQ
005			20240729124609.0
006			m o d |
007			cr cnu||||||||
008			240724s2002 xx o ||||0 eng d
020			_a9781470403300 _q(electronic bk.)
020			_z9780821827390
035			_a(MiAaPQ)EBC3114483
035			_a(Au-PeEL)EBL3114483
035			_a(CaPaEBR)ebr11041261
035			_a(OCoLC)922964856
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA377 -- .D64 2002eb
082	0		_a510 s;515/.353
100	1		_aDoelman, Arjen.
245	1	0	_aStability Index Analysis of 1-D Patterns of the Gray-Scott Model.
250			_a1st ed.
264		1	_aProvidence : _bAmerican Mathematical Society, _c2002.
264		4	_c©2002.
300			_a1 online resource (82 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aMemoirs of the American Mathematical Society ; _vv.155
505	0		_aIntro -- Contents -- Preface -- Chapter 1. Introduction -- 1.1. The Gray-Scott Model: Background -- 1.2. Asymptotic Analysis of the Wave -- 1.3. The Nonlocal Eigenvalue Problem (NLEP) -- 1.4. The Main Results -- Chapter 2. The Evans Function and the Stability Index -- 2.1. The Linearized Equations -- 2.2. The Evans Function -- 2.3. The Stability Index -- 2.4. Outline and Endgame of the Proof -- Chapter 3. Tracking the Fast Subbundle -- 3.1. Asymptotic and Reduced Equations in the Fast Scaling -- 3.2. A Large λ Estimate -- 3.3. Invariant Sets for the Projectivized Flow -- 3.4. Corollaries of the Fast Tracking Theorem -- Chapter 4. The Slow Subbundle -- 4.1. Definition of the Slow Solution -- 4.2. Tracking the Slow Solution over the Slow Fields -- 4.3. Tracking the Slow Solution over the Fast Field -- 4.4. The Construction of ε[sub(8)] (K,δ) -- Chapter 5. Calculation of the Stability Index -- 5.1. The Strongly Unstable Regime: 0≤β&lt -- 1/2 -- 5.2. The Other Regimes: 1/2≤β&lt -- 1 -- Chapter 6. Concluding Remarks -- Bibliography.
588			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650		0	_aReaction-diffusion equations.
650		0	_aPerturbation (Mathematics).
650		0	_aEigenvalues.
655		4	_aElectronic books.
700	1		_aGardner, Robert A.
700	1		_aKaper, Tasso J.
776	0	8	_iPrint version: _aDoelman, Arjen _tStability Index Analysis of 1-D Patterns of the Gray-Scott Model _dProvidence : American Mathematical Society,c2002 _z9780821827390
797	2		_aProQuest (Firm)
830		0	_aMemoirs of the American Mathematical Society
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3114483 _zClick to View
999			_c69978 _d69978