4 research outputs found
Nonlinear stability of the composite wave of planar rarefaction waves and planar contact waves for viscous conservation laws with non-convex flux under multi-dimensional periodic perturbations
In this paper, we study the nonlinear stability of the composite wave
consisting of planar rarefaction and planar contact waves for viscous
conservation laws with degenerate flux under multi-dimensional periodic
perturbations. To the level of our knowledge, it is the first stability result
of the composite wave for conservation laws in several dimensions. Moreover,
the perturbations studied in the present paper are periodic, which keep
constantly oscillating at infinity. Suitable ansatz is constructed to overcome
the difficulty caused by this kind of perturbation and delicate estimates are
done on zero and non-zero modes of perturbations. We obtain satisfactory decay
rates for zero modes and exponential decay rates for non-zero modes