Cauchy problem for the complex Ginzburg-Landau type Equation with $L^{p}$-initial data

Daisuke Shimotsuma; Tomomi Yokota; Kentarou Yoshii

Displaying similar documents to “Cauchy problem for the complex Ginzburg-Landau type Equation with $L^{p}$ -initial data”

Semivariation in $L^{p}$ -spaces

Brian Jefferies, Susumu Okada (2005)

Commentationes Mathematicae Universitatis Carolinae

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Suppose that $X$ and $Y$ are Banach spaces and that the Banach space $X {\hat{\otimes}}_{τ} Y$ is their complete tensor product with respect to some tensor product topology $τ$ . A uniformly bounded $X$ -valued function need not be integrable in $X {\hat{\otimes}}_{τ} Y$ with respect to a $Y$ -valued measure, unless, say, $X$ and $Y$ are Hilbert spaces and $τ$ is the Hilbert space tensor product topology, in which case Grothendieck’s theorem may be applied. In this paper, we take an index $1 \leq p < \infty$ and suppose that $X$ and $Y$ are $L^{p}$ -spaces with $τ_{p}$ the associated...

A zero-two theorem for a certain class of positive contractions in finite dimensional $L^{P}$ -spaces $(1 ⩽ p < + \infty)$

R. Zaharopol (1984)

Annales scientifiques de l'Université de Clermont-Ferrand 2. Série Probabilités et applications

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Ergodic properties of contraction semigroups in $L_{p}$ , $1 < p < \infty$

Ryotaro Sato (1994)

Commentationes Mathematicae Universitatis Carolinae

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Let ${T (t) : t > 0}$ be a strongly continuous semigroup of linear contractions in $L_{p}$ , $1 < p < \infty$ , of a $σ$ -finite measure space. In this paper we prove that if there corresponds to each $t > 0$ a positive linear contraction $P (t)$ in $L_{p}$ such that $| T (t) f | \leq P (t) | f |$ for all $f \in L_{p}$ , then there exists a strongly continuous semigroup ${S (t) : t > 0}$ of positive linear contractions in $L_{p}$ such that $| T (t) f | \leq S (t) | f |$ for all $t > 0$ and $f \in L_{p}$ . Using this and Akcoglu’s dominated ergodic theorem for positive linear contractions in $L_{p}$ , we also prove multiparameter pointwise ergodic and local ergodic...

Displaying similar documents to “Cauchy problem for the complex Ginzburg-Landau type Equation with L p -initial data”

Semivariation in L p -spaces

A zero-two theorem for a certain class of positive contractions in finite dimensional L P -spaces ( 1 ⩽ p &lt; + ∞ )

Ergodic properties of contraction semigroups in L p , 1 < p < ∞

Displaying similar documents to “Cauchy problem for the complex Ginzburg-Landau type Equation with $L^{p}$ -initial data”

Semivariation in $L^{p}$ -spaces

A zero-two theorem for a certain class of positive contractions in finite dimensional $L^{P}$ -spaces $(1 ⩽ p < + \infty)$

Ergodic properties of contraction semigroups in $L_{p}$ , $1 < p < \infty$