Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Initial mixed-boundary value problem for anisotropic fractional
  degenerate parabolic equations   We consider an initial mixed-boundary value problem for anisotropic
fractional type degenerate parabolic equations posed in bounded domains.
Namely, we consider that the boundary of the domain splits into two parts. In
one of them, we impose a Dirichlet boundary condition and in the another one a
Neumann condition. Under this mixed-boundary condition, we show the existence
of solutions for measurable and bounded non-negative initial data. The nonlocal
anisotropic diffusion effect relies on an inverse of a s-fractional type
elliptic operator, and the solvability is proved for any s in (0, 1).

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The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol