Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Properties of Generalized Forchheimer Flows in Porous Media   The nonlinear Forchheimer equations are used to describe the dynamics of
fluid flows in porous media when Darcy's law is not applicable. In this
article, we consider the generalized Forchheimer flows for slightly
compressible fluids and study the initial boundary value problem for the
resulting degenerate parabolic equation for pressure with the time-dependent
flux boundary condition. We estimate $L^\infty$-norm for pressure and its time
derivative, as well as other Lebesgue norms for its gradient and second spatial
derivatives. The asymptotic estimates as time tends to infinity are emphasized.
We then show that the solution (in interior $L^\infty$-norms) and its gradient
(in interior $L^{2-\delta}$-norms) depend continuously on the initial and
boundary data, and coefficients of the Forchheimer polynomials. These are
proved for both finite time intervals and time infinity. The De Giorgi and
Ladyzhenskaya-Uraltseva iteration techniques are combined with uniform
Gronwall-type estimates, specific monotonicity properties, suitable parabolic
Sobolev embeddings and a new fast geometric convergence result.

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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom