Cholewa J., Dlotko T. — Global Attractors in Abstract Parabolic Problems (London Mathematical Society Lecture Note Series) :: Электронная библиотека попечительского совета мехмата МГУ

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Cholewa J., Dlotko T. — Global Attractors in Abstract Parabolic Problems (London Mathematical Society Lecture Note Series)

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Название: Global Attractors in Abstract Parabolic Problems (London Mathematical Society Lecture Note Series)

Авторы: Cholewa J., Dlotko T.

Аннотация:

The study of dissipative equations has attracted substantial attention over many years. Much progress has been achieved using a combination of both finite dimensional and infinite dimensional techniques. In this book the authors exploit these same ideas to investigate the asymptotic behavior of dynamical systems corresponding to parabolic equations. In particular they present the theory of global attractors in detail. Extensive auxiliary material and rich references make this self-contained book a suitable introduction for graduate students.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 245

Добавлена в каталог: 09.08.2014

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Предметный указатель

$X^{s+\alpha}$ solution      148
$X^{\alpha}$ solution, global      70
$X^{\alpha}$ solution, Global mild      163
$X^{\alpha}$ solution, Local      55
$X^{\alpha}$ solution, Local mild      162
Agmon inequalities      25
Ascoli — Arzela criterion      206
Attractor, global      4
Attractor, local      4
Backward uniqueness property      139
Bernoulli inequality      17
Besov spaces      23
Bessel potentials      205
Blow up phenomenon      92
Bochner integral      56
Boundary, $C^{m}$ smooth      207
Caratheodory conditions      208
Cauchy inequality      16
Cauchy integral formula      57
Classical solution      156
Compact resolvent      31
Complementary condition      30
Complex interpolation space      46
Condition, $(A^{'}_{2})$       79 203
Condition, $(A_{1})$       72
Condition, $(A_{2})$       72 203
Condition, $(X^{s+\alpha},X^{s})$       148
Condition, $(\alpha)$       47
Cone condition      207
Dissipativeness condition      105
Dissipativeness condition, local      110
Elliptic boundary value problem      29
Embedding, compact      207
Embedding, continuous      206
Equilibrium      2
Equilibrium, stable      165
Equilibrium, uniformly asymptotically stable      166
Extension operator      207
Extension property      207
Extinction phenomenon      140
Form, coercive      91
Form, symmetric      91
Fractional powers      42
Function, finitely valued      56
Function, increasing      211
Function, little Hoelder continuous      180
Function, nonnegative      211
Gateaux derivative      199
Generalized      208
Gronwall inequality, asymptotic      18
Gronwall inequality, generalized      19
Gronwall inequality, uniform      18
Growth restriction, general      95
Growth restriction, sublinear      70
Hoelder inequality      17
Hoelder semi-norm      206
Imaginary powers      45
Interpolation formula      46
Local Lipschitz condition      90
Lyapunov function      11
Maximum principle      211 216
Moments inequality      46
Net smoothness number      23
Nirenberg — Gagliardo inequality      25
Nonnegative cone      211
Normality condition      30
Operator, aelf-adjoint      40
Operator, bounded below      39
Operator, coercive      195

Operator, hemicontinuous      194
Operator, maximal monotone      195
Operator, monotone      195
Operator, Nemytskii      208
Operator, perturbed      37
Operator, positive      42
Operator, positive definite      40
Operator, product      37
Operator, sectorial      32
Orbit, complete      3
Orbit, negative      2
Orbit, positive      2
Order relation      211
Poincare inequality      95
Regular parabolic i.b.v.p.      181
Resolvent equation      31
Roots condition      29
Semigroup, $C^{0}$       1
Semigroup, analytic      34
Semigroup, asymptotically compact      15
Semigroup, asymptotically smooth      5
Semigroup, bounded dissipative      5
Semigroup, compact      2
Semigroup, completely continuous      14
Semigroup, point dissipative      5
Set, $\omega$ -limit      2
Set, absorbing      2
Set, attracting      2
Set, connected      4
Set, invariant      2
Set, positively invariant      2
Set, separated      4
Set, stable      3
Set, stable, asymptotically      3
Set, stable, uniformly asymptotically      3
Sobolev embeddings for $X^{\alpha}$ spaces      49
Sobolev embeddings for fractional order spaces      24
Sobolev embeddings for natural order space      23
Sobolev embeddings, compact      23
Spaces, $B^{s}_{p,p,\{B_{j}\}}(\Omega)$       31
Spaces, $B^{s}_{p,p}(R^{n})$       23
Spaces, $B^{s}_{p,p}(\Omega)$       23
Spaces, $C^{1+}^{\mu\atop\overline{2m}}^{,2m+\mu}([0,\tau]\times\overline{\Omega})$       181 221
Spaces, $C^{k+\mu}(\overline{\Omega})$       206
Spaces, $C^{k}((0,T),X)$       206
Spaces, $C^{k}(\overline{\Omega})$       206
Spaces, $h^{2m+\mu}_{\{B_{j}\}}(\overline{\Omega})}$       181
Spaces, $H^{2m\alpha}_{p,\{B_{j}\}}(\Omega)$       48
Spaces, $h^{k+\theta}(\overline{\Omega})$       180
Spaces, $H^{m}(\Omega)$       205
Spaces, $h^{s}_{p,\{B_{j}\}}(\Omega)$       31
Spaces, $H^{s}_{p}(R^{n})$       205
Spaces, $H^{s}_{p}(\Omega)$       24
Spaces, $L^{p}(\Omega)$       204
Spaces, $L^{p}(\Omega;\rho)$       204
Spaces, $W^{-m,p'}(\Omega)$       205
Spaces, $W^{1,2m}_{p}((0,\tau)\times\Omega)$       181 219
Spaces, $W^{2m,p}_{\{B_{j}\}}(\Omega)$       31
Spaces, $W^{m,p}(\Omega)$       205
Spaces, $W^{s,p}(R^{n})$       23
Spaces, $W^{s,p}(\Omega)$       24
Spaces, $W^{s,p}_{\{B_{j}\}}(\Omega)$       31
Spaces, $X^{\alpha}$       43
Spaces, $X_{\geq}$       211
Spaces, $\mathcal{L}(X,Y)$       206
Stokes operator      52
Strong Ellipticity Condition      29
Volterra inequality      19
Young inequality      16

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