• search hit 78 of 182
Back to Result List

Non-persistence of heteroclinic orbits in viscous balance laws for vanishing viscosity

Please always quote using this URN:urn:nbn:de:0296-matheon-10189
  • The article investigates the relation between global solutions of hyperbolic balance laws and viscous balance laws on the circle. It is thematically located at the crossroads of hyperbolic and parabolic partial differential equations with one-dimensional space variable and periodic boundary conditions. The two equations are given by: u_t+f(u)_x=g(u) and u_t+f(u)_x=e u_{xx}+g(u). The main result of the paper corrects a result on the persistence of heteroclinic connections by Fan and Hale from 1995 when viscosity vanishes: The "Connection Lemma" states that a connection can only persist if the zero number of the source state is a multiple of the zero number of the target state. The "Cascading Theorem" then yields convergence of heteroclinic connections to a sequence of heteroclinic connections and stationary solutions in case of non-persistence. In addition a full description of the connection problem of rotating waves on the parabolic attractor is given.

Export metadata

Additional Services

Share in Twitter Search Google Scholar
Metadaten
Author:Julia Ehrt
URN:urn:nbn:de:0296-matheon-10189
Referee:Alexander Mielke
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2012/01/25
Release Date:2012/01/25
Tag:heteroclinic orbits; hyperbolic balance law; vanishing viscosity
Institute:Research Center Matheon
Humboldt-Universität zu Berlin
Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Bxx Qualitative properties of solutions / 35B25 Singular perturbations
Preprint Number:880
Verstanden ✔
Diese Webseite verwendet technisch erforderliche Session-Cookies. Durch die weitere Nutzung der Webseite stimmen Sie diesem zu. Unsere Datenschutzerklärung finden Sie hier.