Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Single point gradient blow-up on the boundary for a Hamilton-Jacobi
  equation with $p$-Laplacian diffusion   We study the initial-boundary value problem for the Hamilton-Jacobi equation
with nonlinear diffusion $u_t=\Delta_p u+|\nabla u|^q$ in a two-dimensional
domain for $q>p>2$. It is known that the spatial derivative of solutions may
become unbounded in finite time while the solutions themselves remain bounded.
We show that, for suitably localized and monotone initial data, the gradient
blow-up occurs at a single point of the boundary. Such a result was known up to
now only in the case of linear diffusion ($p=2$). The analysis in the case
$p>2$ is considerably more delicate.

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The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
9
The categories of this paper are: nlin