Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exponential Decay Results for Semilinear Parabolic PDE with $C^0$
  Potentials: A "Mean Value" Approach   The asymptotic behavior of some semilinear parabolic PDEs is analyzed by
means of a "mean value" property. This property allows us to determine, by
means of appropriate {\em{a priori}} estimates, some exponential decay results
for suitable global solutions. We also apply the method to investigate a
well-known finite time blow-up result. An application is given to a
one-dimensional semilinear parabolic PDE with boundary degeneracy. Our results
shed further light onto the problem of determining initial data for which the
corresponding solution is guaranteed to exponentially decay to zero or blow-up
in finite time.

22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
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The categories of this paper are: eess
16
The categories of this paper are: stat
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The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph