Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Continuous dependence estimates for nonlinear fractional
  convection-diffusion equations   We develop a general framework for finding error estimates for
convection-diffusion equations with nonlocal, nonlinear, and possibly
degenerate diffusion terms. The equations are nonlocal because they involve
fractional diffusion operators that are generators of pure jump Levy processes
(e.g. the fractional Laplacian). As an application, we derive continuous
dependence estimates on the nonlinearities and on the Levy measure of the
diffusion term. Estimates of the rates of convergence for general nonlinear
nonlocal vanishing viscosity approximations of scalar conservation laws then
follow as a corollary. Our results both cover, and extend to new equations, a
large part of the known error estimates in the literature.

25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
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The categories of this paper are: econ
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: stat
31
The categories of this paper are: ao-sci
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The categories of this paper are: solv-int