---
res:
bibo_abstract:
- In this paper we develop numerical methods for integrating general evolution equations
u(t) = F(u), u(0) = u(0), where F is defined on a dense subspace of some Banach
space (generally infinite-dimensional) and is equivariant with respect to the
action of a finite-dimensional (not necessarily compact) Lie group. Such equations
typically arise from autonomous PDEs on unbounded domains that are invariant under
the action of the Euclidean group or one of its subgroups. In our approach we
write the solution u(t) as a composition of the action of a time-dependent group
element with a "frozen solution" in the given Banach space. We keep the frozen
solution as constant as possible by introducing a set of algebraic constraints
(phase conditions), the number of which is given by the dimension of the Lie group.
The resulting PDAE (partial differential algebraic equation) is then solved by
combining classical numerical methods, such as restriction to a bounded domain
with asymptotic boundary conditions, half-explicit Euler methods in time, and
finite differences in space. We provide applications to reaction-diffusion systems
that have traveling wave or spiral solutions in one and two space dimensions.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Wolf-Jürgen
foaf_name: Beyn, Wolf-Jürgen
foaf_surname: Beyn
foaf_workInfoHomepage: http://www.librecat.org/personId=12477
- foaf_Person:
foaf_givenName: Vera
foaf_name: Thümmler, Vera
foaf_surname: Thümmler
bibo_doi: 10.1137/030600515
bibo_issue: '2'
bibo_volume: 3
dct_date: 2004^xs_gYear
dct_identifier:
- UT:000222456500001
dct_isPartOf:
- http://id.crossref.org/issn/1536-0040
dct_language: eng
dct_publisher: Society for Industrial and Applied Mathematics@
dct_subject:
- equivariance
- general evolution equations
- Lie groups
- partial
- differential algebraic equations
- unbounded domains
- boundary conditions
- asymptotic
dct_title: Freezing solutions of equivariant evolution equations@
...