Hyperbolic systems of conservation laws

By P. Lax. 2006

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The Existence of Current-Vortex Sheets in Ideal Compressible Magnetohydrodynamics (2009, background): “In [8], using the result of [6], they have also shown the existence of weakly stable shock waves in isentropic gas dynamics.1 In MHD there are two types of Lax shocks: slow and fast shock waves (see, e.g., [18,19]).”
A well posed conservation law with a variable unilateral constraint (2007, background): “[9] K.H. Karlsen, J.D. Towers, Convergence of the Lax–Friedrichs scheme and stability for conservation laws with a discontinous space–time dependent flux, Chinese Ann.”
On the controllability of the 1-D isentropic Euler equation (2007, background): “Note that ∇λi (u) · r̂i (u) -= 0 for any u ∈ R+∗ × R, that is, the two fields are genuinely nonlinear in the sense of Lax (see [25]).”