Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Diffusive Mixing of Stable States in the Ginzburg-Landau Equation   For the time-dependent Ginzburg-Landau equation on the real line, we
construct solutions which converge, as $x \to \pm\infty$, to periodic
stationary states with different wave-numbers $\eta_\pm$. These solutions are
stable with respect to small perturbations, and approach as $t \to +\infty$ a
universal diffusive profile depending only on the values of $\eta_\pm$. This
extends a previous result of Bricmont and Kupiainen by removing the assumption
that $\eta_\pm$ should be close to zero. The existence of the diffusive profile
is obtained as an application of the theory of monotone operators, and the
long-time behavior of our solutions is controlled by rewriting the system in
scaling variables and using energy estimates involving an exponentially growing
damping term.

2
The categories of this paper are: math
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
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The categories of this paper are: physics
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn