http://www.cnr.it/ontology/cnr/individuo/prodotto/ID287481
Invariant manifolds for a singular ordinary differential equation (Articolo in rivista)
- Type
- Label
- Invariant manifolds for a singular ordinary differential equation (Articolo in rivista) (literal)
- Anno
- 2011-01-01T00:00:00+01:00 (literal)
- Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi
- 10.1016/j.jde.2010.11.010 (literal)
- Alternative label
- Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
- Stefano Bianchini; Laura V. Spinolo (literal)
- Pagina inizio
- Pagina fine
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- http://www.sciencedirect.com/science/article/pii/S0022039610004390 (literal)
- Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume
- Rivista
- Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#pagineTotali
- Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroFascicolo
- Note
- ISI Web of Science (WOS) (literal)
- Scopu (literal)
- Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
- SISSA, Via Bonomea 265, 34136 Trieste, Italy;
Ennio De Giorgi Center, Scuola Normale Superiore, Pisa, Italy;
Institute of Mathematics, University of Zurich, Switzerland (literal)
- Titolo
- Invariant manifolds for a singular ordinary differential equation (literal)
- Abstract
- We study the singular ordinary differential equation
dU/dt = F(U)/z(U) + G(U).
The equation is singular because z(U) can attain the value 0. We focus on
the solutions of the above equation that
belong to a small neighbourhood of a point V such that F(U)= G(U) = 0 and
z(U) = 0. We
investigate the existence of manifolds that are locally invariant for the
above equation and that contain orbits with
a prescribed asymptotic behaviour. Under suitable hypotheses on the set {U
: z(U) = 0}, we extend
to the case of the singular ODE the definitions of center manifold,
center-stable manifold and of
uniformly stable manifold. We prove that the solutions of the singular ODE
lying on each of these manifolds are regular: this is not trivial since we
provide examples showing that, in general, a solution of a singular ODE is
not continuously differentiable. Finally, we show a decomposition result
for a center-stable manifold and for the uniformly stable manifold. An
application of our analysis concerns the study of the viscous profiles
with small total variation for a class of mixed hyperbolic-parabolic
systems in one space variable. Such a class includes the compressible
Navier Stokes equation. (literal)
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