Propagation of singularities of shock wave type in a~system of equations of two-dimensional pressureless gas dynamics
Matematičeskie zametki, Tome 66 (1999) no. 5, pp. 760-769.

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Yu. G. Rykov. Propagation of singularities of shock wave type in a~system of equations of two-dimensional pressureless gas dynamics. Matematičeskie zametki, Tome 66 (1999) no. 5, pp. 760-769. http://geodesic.mathdoc.fr/item/MZM_1999_66_5_a11/

[1] Zeldovich Ya. B., “Gravitational instability: an approximate theory for large density perturbations”, Astron. Astrophys., 5 (1970), 84–89

[2] Shandarin S. F., Zeldovich Ya. B., “The large-scale structure of the Universe: turbulence, intermittency, structures in a self-gravitating medium”, Rev. Modern Phys., 61:2 (1989), 185–220 | DOI | MR

[3] Bouchut F., “On zero-pressure gas dynamics”, Advances in Kinetic Theory and Computing, Series on Advances in Mathematics and Applied Sciences, 22, World Scientific, 1994, 171–190 | MR | Zbl

[4] Veinan I., Rykov Yu. G., Sinai Ya. G., “Variatsionnyi printsip Laksa–Oleinik dlya nekotorykh odnomernykh sistem kvazilineinykh uravnenii”, UMN, 50:1 (1995), 193–194 | MR | Zbl

[5] Weinan E., Rykov Yu. G., Sinai Ya. G., “Generalized variational principles, global weak solutions and behavior with random initial data for systems of conservation laws arising in adhesion particle dynamics”, Comm. Math. Phys., 177 (1996), 349–380 | DOI | MR

[6] Grenier E., “Existence globale pour le système des gas sans pression”, C. R. Acad. Sci. Paris. Sér. 1, 321 (1995), 171–174 | MR | Zbl

[7] Hopf E., “The partial differential equation $u_t+uu_x=\mu u_{xx}$”, Comm. Pure Appl. Math., 3:3 (1950), 201–230 | DOI | MR | Zbl

[8] Lax P. D., “Weak solutions of nonlinear hyperbolic equations and their numerical computation”, Comm. Pure Appl. Math., 7:1 (1954), 159–193 | DOI | MR | Zbl

[9] Lax P. D., “Hyperbolic systems of conservation laws”, Comm. Pure Appl. Math., 10:4, 537–566 | DOI | MR | Zbl

[10] Oleinik O. A., “Zadacha Koshi dlya nelineinykh differentsialnykh uravnenii pervogo poryadka s razryvnymi nachalnymi usloviyami”, Tr. MMO, 5, URSS, M., 1956, 433–454 | MR | Zbl

[11] Majda A., “Compressible fluid flow and systems of conservation laws in several space variables”, Appl. Math. Sci., 53 (1984), 1–159 | MR

[12] DiPerna R. J., “Compensated compactness and general systems of conservation laws”, Trans. Amer. Math. Soc., 292:2 (1985), 383–420 | DOI | MR

[13] Zhang T., Zheng Y. X., “Conjecture on structure of solutions of Riemann problem for 2-D gas dynamic systems”, SIAM J. Math. Anal., 21:3 (1990), 593–630 | DOI | MR | Zbl