Preprint of the project: SFB 343: Discrete structures in mathematics

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.