A random dispersion Schr枚dinger equation with time-oscillating nonlinearity

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• 作者：Daoyuan Fang ^{dyf@zju.edu.cn" class="auth_mail} ; Linzi Zhang ^{linzi0116@gmail.com" class="auth_mail} ; Ting Zhang ; ^{zhangting79@zju.edu.cn" class="auth_mail}
• 关键词：Random dispersion ; Nonlinear Schrö ; dinger equation ; Time-oscillating nonlinearity
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：1 October 2014
• 年：2014
• 卷：418
• 期：1
• 页码：403-414
• 全文大小：304 K

文摘

In this paper, we consider the nonlinear Schrödinger equation with the random dispersion and time-oscillating nonlinearity, where m   satisfying some ergodic conditions and 胃   a periodic function. We prove that the solution u_蔚$u_{蔚}$ converges as 蔚→0$蔚\to 0$ to the solution of the limit equation with the initial datum u₀$u_0$ in H¹(R)$H^1(\mathbb{R})$. And the convergence holds in the sense of distribution in C([0,T];H¹(R))$C([0,T];H^1(\mathbb{R}))$, T<蟿^{鈦?/sup>(u₀)}$T<{蟿}^{鈦?/mo>}(u_0)$ almost surely, where 蟿^{鈦?/sup>(u₀)}${蟿}^{鈦?/mo>}(u_0)$ is the maximal existence time for the limit equation.