Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Instability of an equilibrium with negative definite linearization   A nonlinear parabolic differential equation is presented which has at least
one equilibrium. This equilibrium is shown to have a negative definite
linearization, but a spectrum which includes zero. An elementary construction
shows that the equilibrium is not stable.

14
The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th