Displaying similar documents to “Ergodic properties of contraction semigroups in L p , 1 < p < ∞ ”

Cauchy problem for the complex Ginzburg-Landau type Equation with L p -initial data

Daisuke Shimotsuma, Tomomi Yokota, Kentarou Yoshii (2014)

Mathematica Bohemica

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This paper gives the local existence of mild solutions to the Cauchy problem for the complex Ginzburg-Landau type equation ∂ u ∂ t - ( λ + i α ) Δ u + ( κ + i β ) | u | q - 1 u - γ u = 0 in ℝ N × ( 0 , ∞ ) with L p -initial data u 0 in the subcritical case ( 1 ≤ q < 1 + 2 p / N ), where u is a complex-valued unknown function, α , β , γ , κ ∈ ℝ , λ > 0 , p > 1 , i = - 1 and N ∈ ℕ . The proof is based on the L p - L q estimates of the linear semigroup { exp ( t ( λ + i α ) Δ ) } and usual fixed-point argument.

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 ⊗ ^ 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 ⊗ ^ 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 ≤ p < ∞ and suppose that X and Y are L p -spaces with τ p the associated...