Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An abstract framework for parabolic PDEs on evolving spaces   We present an abstract framework for treating the theory of well-posedness of
solutions to abstract parabolic partial differential equations on evolving
Hilbert spaces. This theory is applicable to variational formulations of PDEs
on evolving spatial domains including moving hypersurfaces. We formulate an
appropriate time derivative on evolving spaces called the material derivative
and define a weak material derivative in analogy with the usual time derivative
in fixed domain problems; our setting is abstract and not restricted to
evolving domains or surfaces. Then we show well-posedness to a certain class of
parabolic PDEs under some assumptions on the parabolic operator and the data.

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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: eess
1
The categories of this paper are: cs
3
The categories of this paper are: physics
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th