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We study the limiting behavior of systems of hyperbolic conservation laws with stiff relaxation terms. Reduced systems, inviscid and viscous local conservation laws, and weakly nonlinear limits are derived through asymptotic expansions. An entropy condition is introduced for N × N systems that ensures the hyperbolicity of the reduced inviscid system. The(More)
We show that the weak detonation waves for a combustion model of Rosales-Majda are nonlinearly stable. Because of the strongly non-linear nature of the wave, usual stability analysis of weakly nonlinear nature does not apply. The chemical switch on-oo is the main feature of nonlinearity. In particular, the propagation of the wave depends sensitively on the(More)
We consider the problem of 2D supersonic flow onto a solid wedge, or equivalently in a concave corner formed by two solid walls. For mild corners, there are two possible steady state solutions, one with a strong and one with a weak shock emanating from the corner. The weak shock is observed in supersonic flights. A long-standing natural conjecture is that(More)
It is shown that expansion waves for the compressible Navier-Stokes equations are nonlinearly stable. The expansion waves are constructed for the compressible Euler equations based on the inviscid Burgers equation. Our result shows that Navier-Stokes equations and Euler equations are time-asymptotically equivalent on the level of expansion waves. The result(More)
We show that the continuum shock prooles for dissipative diierence schemes constructed in Part I are nonlinearly stable. It is shown rst that the prooles have the conservation property, obtained as the limit of the discrete version for prooles with nearby rational, quasi-Diophantine speeds. This allows us to formulate anti-diierencing of the schemes and to(More)
We are interested in the large time behavior of a stationary shock layer under the boundary eeect. It is shown that the stationary shock propagates away from the boundary with speed inversely proportional to the time t. Consequently, the location of the wave front is of order log(1 + t). We show therefore that the viscous and time-asymptotic limits do not(More)