Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fractal Hamilton-Jacobi-KPZ equations   Nonlinear and nonlinear evolution equations of the form $u_t=\L u \pm|\nabla
u|^q$, where $\L$ is a pseudodifferential operator representing the
infinitesimal generator of a L\'evy stochastic process, have been derived as
models for growing interfaces in the case when the continuous Brownian
diffusion surface transport is augmented by a random hopping mechanism. The
goal of this paper is to study properties of solutions to this equation
resulting from the interplay between the strengths of the "diffusive" linear
and "hyperbolic" nonlinear terms, posed in the whole space $\bbfR^N$, and
supplemented with nonnegative, bounded, and sufficiently regular initial
conditions.

37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat