Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global well-posedness, dissipation and blow up for semilinear heat
  equations in energy spaces associated with self-adjoint operators   The purpose in this paper is to determine the global behavior of solutions to
the initial-boundary value problems for energy-subcritical and critical
semilinear heat equations by initial data with lower energy than the mountain
pass level in energy spaces associated with self-adjoint operators satisfying
Gaussian upper bounds. Our self-adjoint operators include the Dirichlet
Laplacian on an open set, Robin Laplacian on an exterior domain, and
Schr\"odinger operators, etc.

21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat