000			04174nam a22003978i 4500
001			CR9780511526404
003			UkCbUP
005			20200124160232.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			090407s2000||||enk o ||1 0|eng|d
020			_a9780511526404 (ebook)
020			_z9780521794244 (paperback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA614.813 _b.C48 2000
082	0	0	_a514/.74 _221
100	1		_aCholewa, Jan W., _eauthor.
245	1	0	_aGlobal attractors in abstract parabolic problems / _cJan W. Cholewa & Tomasz Dlotko ; in cooperation with Nathaniel Chafee.
264		1	_aCambridge : _bCambridge University Press, _c2000.
300			_a1 online resource (xii, 235 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aLondon Mathematical Society lecture note series ; _v278
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0		_aCh. 1. Preliminary Concepts -- 1.1. Elements of stability theory -- 1.2. Inequalities. Elliptic operators -- 1.3. Sectorial operators -- Ch. 2. The abstract Cauchy problem -- 2.1. Evolutionary equation with sectorial operator -- 2.2. Variation of constants formula -- 2.3. Local X[superscript [alpha]] solutions -- Ch. 3. Semigroups of global solutions -- 3.1. Generation of nonlinear semigroups -- 3.2. Smoothing properties of the semigroup -- 3.3. Compactness results -- Ch. 4. Construction of the global attractor -- 4.1. Dissipativeness of {T(t)} -- 4.2. Existence of a global attractor -- abstract setting -- 4.3. Global solvability and attractors in X[superscript [alpha]] scales -- Ch. 5. Application of abstract results to parabolic equations -- 5.1. Formulation of the problem -- 5.2. Global solutions via partial information -- 5.3. Existence of a global attractor -- Ch. 6. Examples of global attractors in parabolic problems -- 6.1. Introductory example -- 6.2. Single second order dissipative equation -- 6.3. The method of invariant regions -- 6.4. The Cahn-Hilliard pattern formation model -- 6.5. Burgers equation -- 6.6. Navier-Stokes equations in low dimension (n [less than or equal to] 2) -- 6.7. Cauchy problems in the half-space R[superscript +] x R[superscript n] -- Ch. 7. Backward uniqueness and regularity of solutions -- 7.1. Invertible processes -- 7.2. X[superscript s+[alpha]] solutions; s [greater than or equal to] 0, [alpha][Epsilon](0,1) -- Ch. 8. Extensions -- 8.1. Non-Lipschitz nonlinearities -- 8.2. Application of the principle of linearized stability -- 8.3. The n-dimensional Navier-Stokes system -- 8.4. Parabolic problems in Holder spaces -- 8.5. Dissipativeness in Holder spaces -- 8.6. Equations with monotone operators -- Ch. 9. Appendix -- 9.1. Notation, definitions and conventions -- 9.2. Abstract version of the maximum principle -- 9.3. L[superscript [infinity]]([Omega]) estimate for second order problems -- 9.4. Comparison of X[superscript [alpha]] solution with other types of solutions -- 9.5. Final remarks.
520			_aThe study of dissipative equations is an area that has attracted substantial attention over many years. Much progress has been achieved using a combination of both finite dimensional and infinite dimensional techniques, and in this book the authors exploit these same ideas to investigate the asymptotic behaviour of dynamical systems corresponding to parabolic equations. In particular the theory of global attractors is presented in detail. Extensive auxiliary material and rich references make this self-contained book suitable as an introduction for graduate students, and experts from other areas, who wish to enter this field.
650		0	_aAttractors (Mathematics)
650		0	_aDifferential equations, Parabolic.
700	1		_aDlotko, Tomasz, _eauthor.
700	1		_aChafee, Nathaniel, _eauthor.
710	2		_aLondon Mathematical Society, _eissuing body.
776	0	8	_iPrint version: _z9780521794244
830		0	_aLondon Mathematical Society lecture note series ; _v278.
856	4	0	_uhttps://doi.org/10.1017/CBO9780511526404
999			_c517720 _d517718