Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dissipative Hyperbolic Geometric Flow   In this paper we introduce and study a new kind of hyperbolic geometric flows
--dissipative hyperbolic geometric flow. This kind of flow is defined by a
system of quasilinear wave equations with dissipative terms. Some interesting
exact solutions are given, in particular, a new concept-- hyperbolic Ricci
soliton is introduced and some of its geometric properties are described. We
also establish the short-time existence and uniqueness theorem for the
dissipative hyperbolic geometric flow, and prove the nonlinear stability of the
flow defined on the Euclidean space of dimension larger than 2. Wave character
of the evolving metrics and curvatures is illustrated and the nonlinear wave
equations satisfied by the curvatures are derived.

29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph