Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence and uniqueness for the mild solution of the stochastic heat
  equation with non-Lipschitz drift on an unbounded spatial domain   We prove the existence and uniqueness of the mild solution for a nonlinear
stochastic heat equation defined on an unbounded spatial domain. The
nonlinearity is not assumed to be globally, or even locally, Lipschitz
continuous. Instead the nonlinearity is assumed to satisfy a one-sided
Lipschitz condition. First, a strengthened version of the Kolmogorov continuity
theorem is introduced to prove that the stochastic convolutions of the
fundamental solution of the heat equation and a spatially homogeneous noise
grow no faster than polynomially. Second, a deterministic mapping that maps the
stochastic convolution to the solution of the stochastic heat equation is
proven to be Lipschitz continuous on polynomially weighted spaces of continuous
functions. These two ingredients enable the formulation of a Picard iteration
scheme to prove the existence and uniqueness of the mild solution.

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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga