Geodesic
Stability of a supersonic flow past a wedge with adjoint weak neutrally stable shock wave
Matematičeskie trudy, Tome 19 (2016) no. 2, pp. 3-41

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We study the classical problem of a supersonic stationary flow of a nonviscous nonheat-conducting gas in local thermodynamic equilibrium past an infinite plane wedge. Under the Lopatinskiĭ­ condition on the shock wave (neutral stability), we prove the well-posedness of the linearized mixed problem (the main solution is a weak shock wave), obtain a representation of the classical solution, where, in this case (in contrast to the case of the uniform Lopatinskiĭ­ condition — an absolutely stable shock wave), plane waves additionally appear in the representation. If the initial data have compact support, the solution reaches the given regime in infinite time. 
@article{MT_2016_19_2_a0,
     author = {A. M. Blokhin and D. L. Tkachev},
     title = {Stability of a supersonic flow past a wedge with adjoint weak neutrally stable shock wave},
     journal = {Matemati\v{c}eskie trudy},
     pages = {3--41},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2016_19_2_a0/}
}
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A. M. Blokhin; D. L. Tkachev. Stability of a supersonic flow past a wedge with adjoint weak neutrally stable shock wave. Matematičeskie trudy, Tome 19 (2016) no. 2, pp. 3-41. http://geodesic.mathdoc.fr/item/MT_2016_19_2_a0/