Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Bi-spaces global attractors in abstract parabolic equations

100%

Cholewa J., Dłotko T.

Banach Center Publications

2003

tom 60

nr 1

13-26

An abstract semilinear parabolic equation in a Banach space X is considered. Under general assumptions on nonlinearity this problem is shown to generate a bounded dissipative semigroup on $X^α$. This semigroup possesses an $(X^α - Z)$-global attractor 𝓐 that is closed, bounded, invariant in $X^α$, and attracts bounded subsets of $X^α$ in a 'weaker' topology of an auxiliary Banach space Z. The abstract approach is finally applied to the scalar parabolic equation in Rⁿ and to the partly dissipative system.

Hyperbolic Equations in Uniform Spaces

100%

Cholewa J., Dlotko T.

Bulletin of the Polish Academy of Sciences. Mathematics

2004

tom 52

nr 3

249-263

The paper is devoted to the Cauchy problem for a semilinear damped wave equation in the whole of ℝ ⁿ. Under suitable assumptions a bounded dissipative semigroup of global solutions is constructed in a locally uniform space $Ḣ¹_{lu}(ℝ ⁿ) × L̇²_{lu}(ℝ ⁿ)$. Asymptotic compactness of this semigroup and the existence of a global attractor are then shown.

Ograniczanie wyników

1 Banach Center Publications

1 Bulletin of the Polish Academy of Sciences. Mathematics

2 Cholewa J.

1 Dlotko T.

1 Dłotko T.

1 2004

1 2003

Wyniki wyszukiwania

Bi-spaces global attractors in abstract parabolic equations

Hyperbolic Equations in Uniform Spaces