Stability of Shock Waves for a Single Conservation Law
نویسنده
چکیده
is piecewise smooth, having jump discontinuities along a finite number of smooth shock curves. (We assume that f is C” and strictly convex.) In this paper we extend the result of [5] to show that generically the topological and differentiable structure of the shock set is unaffected by small perturbations of the initial data. As in [5] we consider initial data in the Schwartz space, although analogous results hold for periodic initial data. We shall call a solution U, corresponding to initial data 4, stable if there is a neighborhood N of 4 in 9(R) with the following property: for any r& EN there is a diffeomorphism of the halfspace 2 = R x [0, co) ‘which maps the shock set of ui onto that of U. The following theorem is our main result.
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