Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Jordan-Moore-Gibson-Thompson equation: well-posedness with
  quadratic gradient nonlinearity and singular limit for vanishing relaxation
  time   In this paper, we consider the Jordan-Moore-Gibson-Thompson equation, a third
order in time wave equation describing the nonlinear propagation of sound that
avoids the infinite signal speed paradox of classical second order in time
strongly damped models of nonlinear acoustics, such as the Westervelt and the
Kuznetsov equation. We show well-posedness in an acoustic velocity potential
formulation with and without gradient nonlinearity, corresponding to the
Kuznetsov and the Westervelt nonlinearities, respectively. Moreover, we
consider the limit as the parameter of the third order time derivative that
plays the role of a relaxation time tends to zero, which again leads to the
classical Kuznetsov and Westervelt models. To this end, we establish
appropriate energy estimates for the linearized equations and employ
fixed-point arguments for well-posedness of the nonlinear equations. The
theoretical results are illustrated by numerical experiments.

9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th