Topics in numerical linear algebra and discrete dynamical systems
00-019 Mingyou Huang.
On Nonlinear Stability of Strong Shock Profiles in
Viscous Conservation Laws
The paper mainly concerns stability
problem of strong shock profiles in viscous conservation laws.
An example of 2x2 system in isentropic gas dynamics is
discussed. First by using a simple geometric argument we prove
that this system has two kinds of strong shock profiles and
based on results of G. Kreiss-H.O. Kreiss and of K. ZumbrunP.
Howard,we show that these shock profiles are nonlinearly stable
if and only if they are linearly asymptotic stable. In
addition, we identify that in the scale of standard Lax shock
profiles,the criteria in [4] and in [9] for nonlinear stability
are equivalent.
