TY - GEN A1 - Ehrt, Julia T1 - Non-persistence of heteroclinic orbits in viscous balance laws for vanishing viscosity N2 - 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. KW - heteroclinic orbits KW - vanishing viscosity KW - hyperbolic balance law Y1 - 2012 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/1018 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-10189 ER -