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Criterion of non-existence or nonuniqueness of solutions to self-similar problems of continuum mechanics. (English. Russian original) Zbl 1026.35077
J. Appl. Math. Mech. 65, No. 6, 941-950 (2001); translation from Prikl. Mat. Mekh. 65, No. 6, 971-982 (2001).
The authors discuss systems of hyperbolic partial equations which describe the conservation laws [see P. D. Lax, Commun. Pure Appl. Math. 10, 537-566 (1957; Zbl 0081.08803)]. Sufficient conditions are presented under which the solution of the self-similar problem on disintegration of an arbitrary discontinuity (or the problem on “piston”) either does not exist or is not unique.
35L65 Hyperbolic conservation laws
35L40 First-order hyperbolic systems
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