Stability analysis of periodic solutions of viscous conservation laws.

摘要

Nonclassical viscous conservation laws arising in multiphase fluid and solid mechanics exhibit a rich variety of traveling wave phenomena, including homoclinic (pulse-type) and periodic solutions along with the standard heteroclinic (shock-type) solutions. Here, we investigate stability of periodic traveling We show that analytic instability of small and large amplitude periodic waves, numerical instability of intermediate amplitude periodic waves for model examples, and pointwise bounds in the case of spectral stability.