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.
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页码：196 / 223
页数：28
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