Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cauchy problem for thermoelastic plate equations with different damping
  mechanisms   In this paper we study Cauchy problem for thermoelastic plate equations with
friction or structural damping in $\mathbb{R}^n$, $n\geq1$, where the heat
conduction is modeled by Fourier's law. We explain some qualitative properties
of solutions influenced by different damping mechanisms. We show which damping
in the model has a dominant influence on smoothing effect, energy estimates,
$L^p-L^q$ estimates not necessary on the conjugate line, and on diffusion
phenomena. Moreover, we derive asymptotic profiles of solutions in a framework
of weighted $L^1$ data. In particular, sharp decay estimates for lower bound
and upper bound of solutions in the $\dot{H}^s$ norm ($s\geq0$) are shown.

20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex