On stability of shock waves in magnetohydrodynamics with anisotropic pressure (Q1335950)

The article is devoted to the study of well-posedness for some linear mixed stability problems for shock waves in magnetohydrodynamics with anisotropic pressure. We derive an a priori estimate for a solution to the stability problem for a fast parallel shock wave in anisotropic magnetohydrodynamics with high pressure. A similar result is discussed for the stability problem for a fast transverse shock wave. Finally, we study instability of a slow magnetohydrodynamic shock wave in magnetohydrodynamics with anisotropic pressure; namely, we construct an example of ill-posedness similar to Hadamard's example for the stability problems for a slow parallel shock wave in the case of a cold plasma.