Strong viscous shocks for systems of conservation laws with a high order of dissipation
The author considers viscous shock profiles for systems of conservation laws with an entropy function. These systems can be written in gradient- flux form \[ (f_ u(u))_ t+(g_ u(u))_ x=0, \] where f and g are scalar functions. Viscous profiles are travelling waves solutions of an associated parabolic system, that approximate shock waves and are determined as tajectories of an autonomous system of ordinary differential equations. Topological methods, in particular the Conley index, are applied to the associated system of ordinary differential equations. For such a treatment, there are various assumptions on the regularity and global behavior of the fluxes f and g.
autonomous system of ordinary differential equations
scientific article; zbMATH DE number 4101743
scientific article