Hopf bifurcation from viscous shock waves

Björn Sandstede, Arnd Scheel

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


Using spatial dynamics, we prove a Hopf bifurcation theorem for viscous Lax shocks in viscous conservation laws. The bifurcating viscous shocks are unique (up to time and space translation), exponentially localized in space, periodic in time, and their speed satisfies the Rankine-Hugoniot condition. We also prove an "exchange of spectral stability" result for super- and subcritical bifurcations and outline how our proofs can be extended to cover degenerate, over-, and undercompressive viscous shocks.

Original languageEnglish (US)
Pages (from-to)2033-2052
Number of pages20
JournalSIAM Journal on Mathematical Analysis
Issue number6
StatePublished - 2008


  • Hopf bifurcation
  • Lax shock
  • Viscous conservation law


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