Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Boundary controllability for a one-dimensional heat equation with a
  singular inverse-square potential   We analyze controllability properties for the one-dimensional heat equation
with singular inverse-square potential $$ u_t-u_{xx}-\frac{\mu}{x^2}u=0,\;\;\;
(x,t)\in(0,1)\times(0,T).$$ For any $\mu<1/4$, we prove that the equation is
null controllable through a boundary control $f\in H^1(0,T)$ acting at the
singularity point $x=0$. This result is obtained employing the moment method by
Fattorini and Russell.

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The categories of this paper are: quant-ph
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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: funct-an
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The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex