Damped wave equation in the subcritical case
Damped wave equation in the subcritical case
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DOI：
10.1016/j.jde.2004.06.018
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发表时间：
2004-12
影响因子：
2.4
通讯作者：
N. Hayashi;E. Kaikina;P. Naumkin
中科院分区：
文献类型：
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作者：
N. Hayashi;E. Kaikina;P. Naumkin
在次临界情形σ∈2-ɛ3，2下研究了一维非线性阻尼波方程柯西问题小解的大时间渐近性.我们假设初值[公式]，∈0，1，其中我们还假设初值的平均值存在一个正值ɛ，使得柯西问题(1)有唯一的整体解Vt，x∈C0，∞；L∞∩L1，a，满足下列时间衰减估计：对于大t>；0，这里2-ɛ3<；σ<；2.
We study large time asymptotics of small solutions to the Cauchy problem for the one dimensional nonlinear damped wave equationin the sub critical case σ∈2-ɛ3,2. We assume that the initial data [Formula: see text] , a∈0,1 where Also we suppose that the mean value of initial data Then there exists a positive value ɛ such that the Cauchy problem (1) has a unique global solution vt,x∈C0,∞;L∞∩L1,a, satisfying the following time decay estimate: for large t>0, here 2-ɛ3<σ<2.