Wyniki wyszukiwania - BazTech

Ograniczanie wyników

2 Bulletin of the Polish Academy of Sciences. Mathematics

Znaleziono wyników: 2

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: absorbing set

Sortuj według:

Ogranicz wyniki do:

Global Attractor for a Fourth-Order Parabolic Equation Modeling Epitaxial Thin Film Growth

Duan N., Zhao X.

Bulletin of the Polish Academy of Sciences. Mathematics

2012

Vol. 60, no 3

259--268

This paper is concerned with a fourth-order parabolic equation which models epitaxial growth of nanoscale thin films. Based on the regularity estimates for semigroups and the classical existence theorem of global attractors, we prove that the fourth order parabolic equation possesses a global attractor in a subspace of H2, which attracts all the bounded sets of H2 in the H2-norm.

Hyperspaces of finite sets in universal spaces for absolute Borel classes

Mine K., Sakai K., Yaguchi M.

Bulletin of the Polish Academy of Sciences. Mathematics

2005

Vol. 53, no 4

409-419

By Fin(X) (resp. Fink (X)), we denote the hyperspace of all non-empty finite subsets of X (resp. consisting of at most k points) with the Vietoris topology. Let ℓ2 (τ) be the Hilbert space with weight τ and ℓf2 (τ) the linear span of the canonical orthonormal basis of ℓ2 (τ). It is shown that if E = ℓf2 (τ) or E is an absorbing set in ℓ2 (τ) for one of the absolute Borel classes aα (τ) and Mα (τ) of weight ≤ τ (α > 0) then Fin(E) and each Fink (E) are homeomorphic to E. More generally, if X is a connected E-manifold then Fin(X) is homeomorphic to E and each Fink (X) is a connected E-manifold.