On the existence time for the Kirchhoff equation with periodic boundary conditions

被引：7

作者：

Baldi, Pietro ^{[1
]}

Haus, Emanuele ^{[2
]}

机构：

[1] Univ Napoli Federico II, Dipartimento Matemat & Applicaz R Caccioppoli, Via Cintia, I-80126 Naples, Italy

[2] Univ Roma Tre, Dipartimento Matemat & Fis, I-00146 Rome, Italy

来源：

NONLINEARITY | 2020年 / 33卷 / 01期

关键词：

Kirchhoff equation; quasilinear wave equations; Cauchy problems; normal forms; quasilinear normal forms; long-time existence; GRAVITY WATER-WAVES; KLEIN-GORDON EQUATIONS; GLOBAL WELL-POSEDNESS; SOBOLEV NORMS; NORMAL FORMS; GROWTH; PERTURBATIONS; SOLVABILITY; STABILITY; DOMAINS;

D O I：

10.1088/1361-6544/ab4c7b

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the Cauchy problem for the Kirchhoff equation on with initial data of small amplitude in Sobolev class. We prove a lower bound for the existence time, which improves the bound given by the standard local theory. The proof relies on a normal form transformation, preceded by a nonlinear transformation that diagonalizes the operator at the highest order, which is needed because of the quasilinear nature of the equation.

引用

页码：196 / 223

页数：28

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