Existence of quasilinear relaxation shock profiles in systems with characteristic velocities
Guy Métivier, Benjamin Texier, Kevin Zumbrun (2012)
Annales de la faculté des sciences de Toulouse Mathématiques
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We revisit the existence problem for shock profiles in quasilinear relaxation systems in the case that the velocity is a characteristic mode, implying that the profile ODE is degenerate. Our result states existence, with sharp rates of decay and distance from the Chapman–Enskog approximation, of small-amplitude quasilinear relaxation shocks. Our method of analysis follows the general approach used by Métivier and Zumbrun in the semilinear case, based on Chapman–Enskog expansion and the...