Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Dynamics of a Degenerate Parabolic Equation: Global Bifurcation
  of Stationary States and Convergence   We study the dynamics of a degenerate parabolic equation with a variable,
generally non-smooth diffusion coefficient, which may vanish at some points or
be unbounded. We show the existence of a global branch of nonnegative
stationary states, covering both the cases of a bounded and an unbounded
domain. The global bifurcation of stationary states, implies-in conjuction with
the definition of a gradient dynamical system in the natural phase space-that
at least in the case of a bounded domain, any solution with nonnegative initial
data tends to the trivial or the nonnegative equilibrium. Applications of the
global bifurcation result to general degenerate semilinear as well as to
quasilinear elliptic equations, are also discussed.

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The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: stat
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex