L1-contraction in viscous scalar conser vation laws: Unconditional stability

30 November 2009
Several dissipative scalar conservation laws share the properties of $L1$-contraction and maximum principle. Stability issues are naturally posed in terms of the $L1$-distance. It turns out that constants and travelling waves are asymptotically stable under zero-mass initial disturbances. For this to happen, we do not need any assumption (smallness of the TW, regularity/smallness of the disturbance, tail asymptotics, non characteristicity, ...) The counterpart is the lack of a decay rate.
  • Partial Differential Equations Seminar