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Cauchy problems in weighted Lebesgue spaces

Jan W. Cholewa, Tomasz Dłotko (2004)

Czechoslovak Mathematical Journal

Global solvability and asymptotics of semilinear parabolic Cauchy problems in $ℝ^{n}$ are considered. Following the approach of A. Mielke [15] these problems are investigated in weighted Sobolev spaces. The paper provides also a theory of second order elliptic operators in such spaces considered over $ℝ^{n}$ , $n \in ℕ$ . In particular, the generation of analytic semigroups and the embeddings for the domains of fractional powers of elliptic operators are discussed.

Characterization of the generators of $C_{0}$ semigroups which leave a convex set invariant

H. N. Bojadziev (1984)

Commentationes Mathematicae Universitatis Carolinae

Comment on “A strong convergence of a generalized iterative method for semigroups of nonexpansive mappings in Hilbert spaces”.

Golkarmanesh, Farman, Naseri, Saber (2011)

Fixed Point Theory and Applications [electronic only]

Common fixed points for Lipschitzian semigroups.

Lahrech, Samir, Mbarki, Abderrahim, Ouahab, Abdelmalek (2006)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Common fixed points of one-parameter nonexpansive semigroups in strictly convex Banach spaces.

Suzuki, Tomonari (2006)

Abstract and Applied Analysis

Compact attractor for weakly damped driven Korteweg-de Vries equations on the real line

Ph. Laurençot (1998)

Czechoslovak Mathematical Journal

We investigate the long-time behaviour of solutions to the Korteweg-de Vries equation with a zero order dissipation and an additional forcing term, when the space variable varies over $R$ , and prove that it is described by a maximal compact attractor in $H^{2} (R)$ .