Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-homogeneous initial boundary value problems for the biharmonic
  Schr\"odinger equation on an interval   In this paper we consider the initial boundary value problem (IBVP) for the
nonlinear biharmonic Schr\"odinger 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 $j=0,1$.

13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ