Global existence of smooth solutions for partially dissipative hyperbolic systems with a convex entropy (Articolo in rivista)

Type
Label
  • Global existence of smooth solutions for partially dissipative hyperbolic systems with a convex entropy (Articolo in rivista) (literal)
Anno
  • 2003-01-01T00:00:00+01:00 (literal)
Alternative label
  • Hanouzet B., Natalini R. (2003)
    Global existence of smooth solutions for partially dissipative hyperbolic systems with a convex entropy
    in Archive for rational mechanics and analysis (Print)
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • Hanouzet B., Natalini R. (literal)
Pagina inizio
  • 89 (literal)
Pagina fine
  • 117 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume
  • 169 (literal)
Rivista
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#descrizioneSinteticaDelProdotto
  • Questo lavoro contiene il primo risultato generale a livello internazionale sulla stabilita' dei sistemi iperbolici dissipativi (literal)
Note
  • ISI Web of Science (WOS) (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • HB Uni Bordeaux, NR CNR (literal)
Titolo
  • Global existence of smooth solutions for partially dissipative hyperbolic systems with a convex entropy (literal)
Abstract
  • We consider the Cauchy problem for a general one dimensional $n\times n$ hyperbolic symmetrizable system of balance laws. It is well known that, in many physical examples, for instance for the isentropic Euler system with damping, the dissipation due to the source term may prevent the shock formation, at least for smooth and small initial data. Our main goal is to find a set of general and realistic sufficient conditions to guarantee the global existence of smooth solutions, and possibly to investigate their asymptotic behavior. For systems which are entropy dissipative, a quite natural generalization of the Kawashima condition for hyperbolic-parabolic systems can be given. In this paper, we first propose a general framework to set this kind of problems, by using the so-called entropy variables. Therefore, we pass to prove some general statements about the global existence of smooth solutions, under different sets of conditions. In particular, the present approach is suitable for dealing with most of the physical examples of systems with a relaxation extension. Our main tools will be some refined energy estimates and the use of a suitable version of the Kawashima condition. (literal)
Prodotto di
Autore CNR
Insieme di parole chiave

Incoming links:


Prodotto
Autore CNR di
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#rivistaDi
Insieme di parole chiave di
data.CNR.it