区间上双调和薛定谔方程的非齐次initial boundary value problems
Non-homogeneous initial boundary value problems for the biharmonic Schrödinger equation on an interval
摘要：
本文考虑了有界区间$(0,L)$上的非线性双调和薛定谔方程的初边值问题，分别具有非齐次Navier或Dirichlet边界条件.对于Navier边界IBVP，如果初始数据位于$H^s(0, L)$中，且$s\geq 0$和$s\neq n+1/2, n\in \mathbb{N}$，并且边界数据是从具有最优解的适当空间中选择的，即，在$H_{loc}^{(s+3-j)/4}(\mathbb {R}^+)$中为$j=0,2$选择$j$阶数据。对于Dirichlet边界IBVP，当$s>10/7$和$s\neq n+1/2, n\in \mathbb{N}$，边界数据从具有最优解的适当空间中选取时，得到了相应的局部适定性，在$H_{loc}^{(s+3-j)/4}(\mathbb {R}^+)$中为$j=0,1$选择$j$阶数据。
英文摘要：
In this paper we consider the initial boundary value problem (IBVP) for the nonlinear biharmonic Schrödinger equation posed on a bounded interval $(0,L)$ with non-homogeneous Navier or Dirichlet boundary conditions, respectively. For Navier boundary IBVP, we set up its local well-posedness if the initial data lies in $H^s(0, L)$ with $s\geq 0$ and $s\neq n+1/2, n\in \mathbb{N}$, and the boundary data are selected from the appropriate spaces with optimal regularities, i.e., the $j$-th order data are chosen in $H_{loc}^{(s+3-j)/4}(\mathbb {R}^+)$, for $j=0,2$. For Dirichlet boundary IBVP the corresponding local well-posedness is obtained when $s>10/7$ and $s\neq n+1/2, n\in \mathbb{N}$, and the boundary data are selected from the appropriate spaces with optimal regularities, i.e., the $j$-th order data are chosen in $H_{loc}^{(s+3-j)/4}(\mathbb {R}^+)$, for $j=0,1$.
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