Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analytical validation of a continuum model for the evolution of a
  crystal surface in multiple space dimensions   In this paper we are concerned with the existence of a weak solution to the
initial boundary value problem for the equation $\frac{\partial u}{\partial t}
= \Delta\left(\Delta u\right)^{-3}$. This problem arises in the mathematical
modeling of the evolution of a crystal surface. Existence of a weak solution
$u$ with $\Delta u\geq 0$ is obtained via a suitable substitution. Our
investigations reveal the close connection between this problem and the
equation $\partial_t\rho+\rho^2\Delta^2\rho^3=0$, another crystal surface model
first proposed by H. Al Hajj Shehadeh, R. V. Kohn and J. Weare in Physica D:
Nonlinear Phenomena, bf 240 (2011), no. 21, 1771-1784.

16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas