Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A class of second-order geometric quasilinear hyperbolic PDEs and their
  application in imaging science   In this paper, we study damped second-order dynamics, which are quasilinear
hyperbolic partial differential equations (PDEs). This is inspired by the
recent development of second-order damping systems for accelerating energy
decay of gradient flows. We concentrate on two equations: one is a damped
second-order total variation flow, which is primarily motivated by the
application of image denoising; the other is a damped second-order mean
curvature flow for level sets of scalar functions, which is related to a
non-convex variational model capable of correcting displacement errors in image
data (e.g. dejittering). For the former equation, we prove the existence and
uniqueness of the solution. For the latter, we draw a connection between the
equation and some second-order geometric PDEs evolving the hypersurfaces which
are described by level sets of scalar functions, and show the existence and
uniqueness of the solution for a regularized version of the equation. The
latter is used in our algorithmic development. A general algorithm for
numerical discretization of the two nonlinear PDEs is proposed and analyzed.
Its efficiency is demonstrated by various numerical examples, where simulations
on the behavior of solutions of the new equations and comparisons with
first-order flows are also documented.

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The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess