Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact solutions of nonlinear boundary value problems of the Stefan type   The (1+1)-dimensional nonlinear boundary value problem, modeling the process
of melting and evaporation of metals, is studied by means of the classical Lie
symmetry method. All possible Lie operators of the nonlinear heat equation,
which allow us to reduce the problem to the boundary value problem for the
system of ordinary differential equations, are found. The forms of heat
conductivity coefficients are established when the given problem can be
analytically solved in an explicit form.

7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th