Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the convergence of the nonlocal nonlinear model to the classical
  elasticity equation   We consider a general class of convolution-type nonlocal wave equations
modeling bidirectional propagation of nonlinear waves in a continuous medium.
In the limit of vanishing nonlocality we study the behavior of solutions to the
Cauchy problem. We prove that, as the kernel functions of the convolution
integral approach the Dirac delta function, the solutions converge strongly to
the corresponding solutions of the classical elasticity equation. An energy
estimate with no loss of derivative plays a critical role in proving the
convergence result. As a typical example, we consider the continuous limit of
the discrete lattice dynamic model (the Fermi-Pasta-Ulam-Tsingou model) and
show that, as the lattice spacing approaches zero, solutions to the discrete
lattice equation converge to the corresponding solutions of the classical
elasticity equation.

8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int