Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Irregular linear systems of PDEs with the conditions on solutions'
  projections   The theory of complete generalized Jordan sets is employed to reduce the PDE
with the irreversible linear operator $B$ of finite index to the regular
problems. It is demonstrated how the question of the choice of boundary
conditions is connected with the $B$-Jordan structure of coefficients of PDE.
The various approaches shows the combination alternative Lyapunov method,
Jordan structure coefficients and skeleton decomposition of irreversible linear
operator from the main part equation are among the most powerfull methods to
attack such challenging problem. On this base the complex problem of the {\it
correct choice of boundary conditions} for the wide class of the singular PDE
can be solved. Aggregated existence and uniqueness theorems can be proved,
solution may continuously depend on the function determied from the
experiments. Such theory can be applied to the integral--differential equations
with partial derivatives.

24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
18
The categories of this paper are: econ
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an