The initial value problem for the cubic nonlinear Klein–Gordon equation
The initial value problem for the cubic nonlinear Klein–Gordon equation
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DOI：
10.1007/s00033-007-7008-8
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发表时间：
2008-11
期刊：
影响因子：
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通讯作者：
N. Hayashi;P. Naumkin
中科院分区：
文献类型：
--
作者：
N. Hayashi;P. Naumkin
We study the initial value problem for the cubic nonlinear Klein–Gordon equation $$ \left\{ \begin{array}{*{20}c} u_{tt} + u-u_{xx} = \mu u^3,\,(t, x)\in {\bf R}\times{\bf R}, \\ u(0) = u_0, u_t(0) = u_1, x\in{\bf R}, \end{array}\quad \quad \quad(0.1) \right. $$ where μ ∈Rand the initial data are real-valued functions. We obtain a sharp asymptotic behavior of small solutions without the condition of a compact support on the initial data which was assumed in the previous works.
We study the initial value problem for the cubic nonlinear Klein–Gordon equation $$ \left\{ \begin{array}{*{20}c} u_{tt} + u-u_{xx} = \mu u^3,\,(t, x)\in {\bf R}\times{\bf R}, \\ u(0) = u_0, u_t(0) = u_1, x\in{\bf R}, \end{array}\quad \quad \quad(0.1) \right. $$ where μ ∈Rand the initial data are real-valued functions. We obtain a sharp asymptotic behavior of small solutions without the condition of a compact support on the initial data which was assumed in the previous works.