Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4624015 | Journal of Mathematical Analysis and Applications | 2006 | 11 Pages |
Abstract
The main contribution of this paper is to use the maximum principle to obtain a lower bound ρϵ⩾C(t,ϵ)>0 for the parabolic system generated by adding “artificial viscosity” to the system of one-dimensional isentropic gas dynamics and to the Euler equations corresponding to the Broadwell model [R.E. Caflisch, Navier–Stokes and Boltzmann shock profiles for a model of gas dynamics, Comm. Pure Appl. Math. 32 (1979) 521–554], where C(t,ϵ) are given explicitly. Here we do not need the restrictions and the periodic initial data used in previous work by other authors.
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