Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homogenization of Hamilton-Jacobi equations with rough time dependence   We consider viscosity solutions of Hamilton-Jacobi equations with oscillatory
spatial dependence and rough time dependence. The time dependence is in the
form of the derivative of a continuous path that converges to a possibly
nowhere-differentiable path, for example a Brownian motion. In the case where
the path is one-dimensional, we prove that the solutions converge locally
uniformly to the solution of a spatially homogenous, stochastic Hamilton-Jacobi
equation in the sense of Lions and Souganidis. We also provide examples of
equations in which the path is multi-dimensional, and show that many different
behaviors are possible, including diverging to infinity or converging in law to
a Brownian motion.

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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: stat
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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: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys