Stable, Oscillatory Viscous Profiles of Weak Shocks in Systems of Stiff Balance Laws
نویسنده
چکیده
This paper is devoted to a phenomenon in hyperbolic balance laws, first described by Fiedler and Liebscher [2], which is similar in spirit to the Turing instability. The combination of two individually stabilising effects can lead to quite rich dynamical behaviour, like instabilities, oscillations, or pattern formation. Our problem is composed of two ingredients. First, we have a strictly hyperbolic conservation law. The second part is a source term which, alone, would describe a simple, stable kinetic behaviour: all trajectories end by converging monotonically to an equilibrium. The balance law, constructed of these two parts, however, can support viscous shock profiles with oscillatory tails. They emerge from a Hopf-like bifurcation point in the associated travelling-wave system. The main result establishes convective stability of oscillatory viscous profiles to weak shocks with extreme speed: if the speed of the wave exceeds any characteristic speed, then the profile is linearly stable in a suitable exponentially weighted space. For intermediate speeds, the profiles are absolutely unstable. This work was supported by the priority research program “Analysis and Numerics for Conservation Laws” of the Deutsche Forschungsgemeinschaft. Oscillatory Viscous Profiles 3
منابع مشابه
Stable, Oscillatory Viscous Profiles of Weak, non-Lax Shocks in Systems of Stiff Balance Laws
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تاریخ انتشار 2003