Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite-dimensional attractors for the quasi-linear strongly-damped wave
  equation   We present a new method of investigating the so-called quasi-linear strongly
damped wave equations $$ \partial_t^2u-\gamma\partial_t\Delta_x u-\Delta_x
u+f(u)= \nabla_x\cdot \phi'(\nabla_x u)+g $$ in bounded 3D domains. This method
allows us to establish the existence and uniqueness of energy solutions in the
case where the growth exponent of the non-linearity $\phi$ is less than 6 and
$f$ may have arbitrary polynomial growth rate. Moreover, the existence of a
finite-dimensional global and exponential attractors for the solution semigroup
associated with that equation and their additional regularity are also
established. In a particular case $\phi\equiv0$ which corresponds to the
so-called semi-linear strongly damped wave equation, our result allows to
remove the long-standing growth restriction $|f(u)|\leq C(1+ |u|^5)$.

17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph