Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Parabolic type equations associated with the Dirichlet form on the
  Sierpinski gasket   By using the analytic tools of Dirichlet forms, we initiate a study of some
non-linear parabolic equations on Sierpinski gasket, motivated by modellings of
fluid flows along a fractal (which can be considered as a simplified rough
porous medium). Unlike the regular spaces case, such equation involving a
convection term must take a quite different form and the convection term must
be singular to the "linear part" which is determined the heat semigroup. In
order to study these parabolic type equations, a new kind of Sobolev
inequalities for the Dirichlet form on the gasket will be established as an
effective tool for our study. These Sobolev inequalities, which are interesting
by their own and in contrast to the case of Euclidean spaces, involve two $L^p$
norms with respect two mutually singular measures. By examining properties of a
singular convolution of the associated heat semigroup, we derive the space-time
regularity of solutions to the parabolic equations under a few technical
conditions. The Burgers equations on the Sierpinski gasket are also studied,
for which a maximum principle for solutions is derived using techniques from
backward stochastic differential equations, and the existence and uniqueness as
well as the regularity of solutions are obtained.

13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
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The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex