Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite time extinction for the 1D stochastic porous medium equation with
  transport noise   We establish finite time extinction with probability one for weak solutions
of the Cauchy-Dirichlet problem for the 1D stochastic porous medium equation
with Stratonovich transport noise and compactly supported smooth initial datum.
Heuristically, this is expected to hold because Brownian motion has average
spread rate $O(t^\frac{1}{2})$ whereas the support of solutions to the
deterministic PME grows only with rate $O(t^{\frac{1}{m{+}1}})$. The rigorous
proof relies on a contraction principle up to time-dependent shift for
Wong-Zakai type approximations, the transformation to a deterministic PME with
two copies of a Brownian path as the lateral boundary, and techniques from the
theory of viscosity solutions.

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The categories of this paper are: physics
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: cs
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys