Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Energy estimates for two-dimensional space-Riesz fractional wave
  equation   The fractional wave equation governs the propagation of mechanical diffusive
waves in viscoelastic media which exhibits a power-law creep, and consequently
provided a physical interpretation of this equation in the framework of dynamic
viscoelasticity. In this paper, we first develop the energy method to estimate
the one-dimensional space-Riesz fractional wave equation. For two-dimensional
cases with the variable coefficients, the discretized matrices are proved to be
commutative, which ensures to carry out of the priori error estimates. The
unconditional stability and convergence with the global truncation error
$\mathcal{O}(\tau^2+h^2)$ are theoretically proved and numerically verified. In
particulary, the framework of the priori error estimates and convergence
analysis are still valid for the compact finite difference scheme and the
nonlocal wave equation.

9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ