Geodesic
Nonuniqueness of a Self-similar Solution to the Riemann Problem for Elastic Waves in Media with a Negative Nonlinearity Parameter
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern Methods of Mechanics, Tome 322 (2023), pp. 251-265

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We study self-similar solutions of the Riemann problem in the nonuniqueness region for weakly anisotropic elastic media with a negative nonlinearity parameter. We show that all discontinuities contained in the solutions in the nonuniqueness region have a stationary structure. We also show that in the nonuniqueness region one can construct two types of self-similar solutions.
Keywords: shock waves, Riemann problem, nonuniqueness of self-similar solutions. 
@article{TM_2023_322_a19,
     author = {A. P. Chugainova and R. R. Polekhina},
     title = {Nonuniqueness of a {Self-similar} {Solution} to the {Riemann} {Problem} for {Elastic} {Waves} in {Media} with a {Negative} {Nonlinearity} {Parameter}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {251--265},
     publisher = {mathdoc},
     volume = {322},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2023_322_a19/}
}
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A. P. Chugainova; R. R. Polekhina. Nonuniqueness of a Self-similar Solution to the Riemann Problem for Elastic Waves in Media with a Negative Nonlinearity Parameter. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern Methods of Mechanics, Tome 322 (2023), pp. 251-265. http://geodesic.mathdoc.fr/item/TM_2023_322_a19/