An inertial manifold and the principle of spatial averaging

Kwean, Hyuk-Jin

doi:10.1155/s0161171201006536

Cited by 2 publications

(3 citation statements)

References 4 publications

(9 reference statements)

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“…Приведем перечень (разумеется, не окончательный) параболических задач, обладающих инерциальным многообразием типа графика (см. [9]- [14]) для 1 * )-4 * ) или же демонстрирующих конечномерную предельную динамику (см. Для случая 4 * ) уточним [13], [14], что в качестве Ω здесь надлежит брать прямоугольник, куб, правильные многоугольники и некоторые другие области с определенного рода симметрией.…”

Section: теорема 42 (основная)unclassified

Эффективная Конечная Параметризация В Фазовых Пространствах Параболических Уравнений

Romanov¹,

Romanov²

2006

Izv. RAN. Ser. Mat.

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Section: теорема 42 (основная)unclassified

Эффективная Конечная Параметризация В Фазовых Пространствах Параболических Уравнений

Romanov¹,

Romanov²

2006

Izv. RAN. Ser. Mat.

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“…(5 * ) The one-dimensional equation of the form (0.5). For (4 * ), we refine the results in [13] and [14]. Namely, a rectangle, a cube, regular polygons and other domains with various kinds of symmetry should be taken as Ω.…”

Section: Proofmentioning

confidence: 99%

“…For example, such a manifold exists for reaction-diffusion equations in some bounded domains Ω ⊂ R N , N 3, and also for the Ginzburg-Landau, Cahn-Hillard, Kuramoto-Sivashinsky, and Kolmogorov-Sivashinsky equations. For more detail, see [9]- [14] and the references there.…”

Section: Introductionmentioning

confidence: 99%

Effective finite parametrization in phase spaces of parabolic equations

Romanov¹

2006

Izv. Math.

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For evolution equations of parabolic type in a Hilbert phase space E, consideration is given to the problem of the effective parametrization (with a Lipschitzian estimate) of the sets K ⊂ E by functionals ϕ1, . . . , ϕm in E * or, in other words, the problem of the linear Lipschitzian embedding of K in R m . If A is the global attractor for the equation, then this kind of parametrization turns out to be equivalent to the finite dimensionality of the dynamics on A. Some tests are established for the parametrization (in various metrics) of subsets in E and, in particular, of manifolds M ⊂ E by linear functionals of different classes. We outline a range of physically significant parabolic problems with a fundamental domain Ω ⊂ R N that admit a parametrization of the elements u(x) ∈ A by their values u(xi) at a finite system of points xi ∈ Ω.

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An inertial manifold and the principle of spatial averaging

Abstract: Abstract. We examine the existence of inertial manifold of a class of differential equations with particular boundary conditions.

Cited by 2 publications

References 4 publications

Эффективная Конечная Параметризация В Фазовых Пространствах Параболических Уравнений

Эффективная Конечная Параметризация В Фазовых Пространствах Параболических Уравнений

Effective finite parametrization in phase spaces of parabolic equations

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