论文标题
BiharmonicSchrödinger方程的非均匀初始边界价值问题间隔
Non-homogeneous initial boundary value problems for the biharmonic Schrödinger equation on an interval
论文作者
论文摘要
在本文中，我们考虑了分别具有非均匀的navier或dirichlet边界条件的有界间隔$（0，l）$的非线性biharmonicschrödinger方程的初始边界值问题（IBVP）。对于Navier Boundare IBVP，如果初始数据位于$ h^s（0，l）$中，则我们设置了其本地适用性，$ s \ geq 0 $和$ s \ s \ neq n+1/2，n \ in \ mathbb {n} $，并且从适当的空间中选择了与最佳规律的适当空间，$ j $。 $ h_ {loc}^{（s+3-j）/4}（\ mathbb {r}^+）$，对于$ j = 0,2 $。对于Dirichlet边界IBVP，当$ s> 10/7 $和$ s \ s \ neq n+1/2，n \ in \ mathbb {n} $中时，获得相应的本地适合性，并且从适当的空间中选择了带有最佳规律性的适当空间，即$ j $ -j $ - the $ j $ - n $ h _}/s loc h _} {s s+h_} {s+h _} { {r}^+）$，对于$ j = 0,1 $。
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 $j=0,1$.
