Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global convergence for ill-posed equations with monotone operators: the
  dynamical systems method   Consider an operator equation $F(u)=0$ in a real Hilbert space.
  Let us call this equation ill-posed if the operator
  $F'(u)$ is not boundedly invertible, and well-posed otherwise.
  If $F$ is monotone $C^2_{loc}(H)$ operator, then we construct a Cauchy
problem, which has the following properties:
  1) it has a global solution for an arbitrary initial data,
  2) this solution tends to a limit as time tends to infinity,
  3) the limit is the minimum norm solution to the equation $F(u)=0$.
  Example of applications to linear ill-posed operator equation is given.

19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph