Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharp ultimate velocity bounds for the general solution of some linear
  second order evolution equation with damping and bounded forcing   We consider a class of linear second order differential equations with
damping and external force. We investigate the link between a uniform bound on
the forcing term and the corresponding ultimate bound on the velocity of
solutions, and we study the dependence of that bound on the damping and on the
"elastic force".
  We prove three results. First of all, in a rather general setting we show
that different notions of bound are actually equivalent. Then we compute the
optimal constants in the scalar case. Finally, we extend the results of the
scalar case to abstract dissipative wave-type equations in Hilbert spaces. In
that setting we obtain rather sharp estimates that are quite different from the
scalar case, in both finite and infinite dimensional frameworks.
  The abstract theory applies, in particular, to dissipative wave, plate and
beam equations.

18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc