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

Title:

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

Creator:

Shimotsuma, Daisuke, Yokota, Tomomi, and Yoshii, Kentarou

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:a8761fd7-79c0-4462-af9b-de9b6d10390f
uuid:a8761fd7-79c0-4462-af9b-de9b6d10390f
doi:10.21136/MB.2014.143860

Subject:

local existence and complex Ginzburg-Landau equation

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

This paper gives the local existence of mild solutions to the Cauchy problem for the complex Ginzburg-Landau type equation ∂u ∂t − (λ + iα)∆u + (κ + iβ)|u| q−1 u − γu = 0 in R N × (0, ∞) with L p -initial data u0 in the subcritical case (1 6 q < 1 + 2p/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 + iα)∆)} and usual fixed-point argument.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

353-361

Source:

Mathematica bohemica | 2014 Volume:139 | Number:2

Harvested from:

CDK

Metadata only:

false