Asymptotic behavior of global solutions to the complex Ginzburg--Landau type equation in the super Fujita-critical case

Autor:	Kusaba, Ryunosuke, Ozawa, Tohru
Rok vydání:	2024
Předmět:	Mathematics - Analysis of PDEs 35Q56 35B40 35C20
Druh dokumentu:	Working Paper
Popis:	We present weighted estimates and higher order asymptotic expansions of global solutions to the complex Ginzburg--Landau (CGL) type equation in the super Fujita-critical case. Our approach is based on commutation relations between the CGL semigroup and monomial weights in $\mathbb{R}^{n}$ for the weighted estimates and on the Taylor expansions with respect to the both space and time variables for the asymptotic expansions. We also characterize the optimal decay rate in time of the remainder for the asymptotic expansion from the viewpoint of the moments of the initial data in space and those of the nonlinear term in spacetime. Comment: 36 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2401.06363 Zobrazit plný text záznamu View this record from Arxiv