Eikonal equation for anisotropic media

A. V. Borovskikh

Trudy Seminara im. I.G. Petrovskogo, Trudy Seminara imeni I. G. Petrovskogo, Tome 29 (2013) no. 29, pp. 162-229

Bibliographie

[1] Kurant R., Uravneniya s chastnymi proizvodnymi, Mir, M., 1964 | MR

[2] Gogoladze V. G., “Volnovoe uravnenie dlya neodnorodnykh i anizotropnykh sred”, Tr. MIAN, 9 (1935), 107–166

[3] Babich V. M., Klimova A. A., “Giperbolicheskoe uravnenie s bolshim parametrom pri mladshikh chlenakh i ierarkhiya voln”, Algebra i analiz, 6:5 (1994), 126–171 | MR

[4] Borovskikh A. V., “Dvumernoe uravnenie eikonala”, Sib. mat. zhurn., 47:5 (2006), 993–1018 | MR | Zbl

[5] Borovskikh A. V., “Uravnenie eikonala v neodnorodnoi srede”, Dokl. RAN, 391:5 (2003), 587–590 | MR | Zbl

[6] Borovskikh A. V., “Gruppovaya klassifikatsiya uravnenii eikonala dlya trekhmernoi neodnorodnoi sredy”, Mat. sb., 195:4 (2004), 23–64 | DOI | MR | Zbl

[7] Borovskikh A. V., “Gruppy ekvivalentnosti uravnenii eikonala i klassy ekvivalentnykh uravnenii”, Vestn. NGU, 2006, no. 4, 3–42 | Zbl

[8] Eizenkhart L. P., Rimanova geometriya, Izd-vo inostr. lit., M., 1948

[9] Ovsyannikov L. V., “Gruppovye svoistva uravneniya S. A. Chaplygina”, PMTF, 1960, no. 3, 126–145

[10] Ovsyannikov L. V., Gruppovoi analiz differentsialnykh uravnenii, Nauka, M., 1978 | MR

[11] Ibragimov N. Kh., Gruppy preobrazovanii v matematicheskoi fizike, Nauka, M., 1983 | MR

[12] Olver P., Prilozheniya grupp Li k differentsialnym uravneniyam, Mir, M., 1989 | MR | Zbl

[13] Ovsyannikov L. V., “Programma PODMODELI. Gazovaya dinamika”, PMM, 58:5 (1994), 30–55 | MR | Zbl

[14] Meleshko S. V., “Odnorodnye avtonomnye sistemy s tremya nezavisimymi peremennymi”, PMM, 58:5 (1994), 97–102 | MR | Zbl

[15] von Weingarten J., “Über die Eigenschaften des Linienelementes der Flächen von constantem Krümmungmass”, J. für Mathematik, 94:3 (1883), 181–202

[16] Bianki L., “Sull'applicatbilitá di due spazi colla medesima curvatura di Riemann constante”, Opere, 9, 7–15

[17] Delgleize A., “Sur les équations de Weingarten et les espaces pseudosphériques”, Bull. Soc. Roy. Sci. Liège, 4:4–5 (1935), 158–161

[18] Fialkov A., “Conformal geodesics”, Trans. Amer. Math. Soc., 45:3 (1939), 443–473 | DOI | MR

[19] Yano K., “Concircular geometry II. Integrability conditions of $\rho_{\mu\nu}=\phi g_{\mu\nu}$”, Proc. Imp. Acad. Tokyo, 16 (1940), 354–360 | DOI | MR

[20] Solodovnikov A. S., “Prostranstva s obschimi geodezicheskimi”, Tr. seminara po vektor. i tenzor. analizu, 11 (1961), 43–102 | MR | Zbl

[21] Solodovnikov A. S., “Proektivnye preobrazovaniya rimanovykh prostranstv”, UMN, 11:4 (1956), 45–116 | MR | Zbl

[22] De Vries H. L., “Über Riemannsche Räume, die infinitesimale konforme Transformationen gestatten”, Math. Z., 60 (1954), 328–347 | DOI | MR | Zbl

[23] Kruchkovich G. I., “O poluprivodimykh rimanovykh prostranstvakh”, DAN SSSR, 115:5 (1957), 862–865 | Zbl

[24] Kruchkovich G. I., “Ob odnom klasse rimanovykh prostranstv”, Tr. seminara po vektor. i tenzor. analizu, 11 (1961), 103–128 | Zbl

[25] Petrov A. Z., Novye metody v obschei teorii otnositelnosti, Nauka, M., 1966 | MR

[26] Dubrovin B. A., Novikov S. P., Fomenko A. T., Sovremennaya geometriya: metody i prilozheniya, Nauka, M., 1986 | MR

[27] Alekseevskii D. V., Vinberg E. V., Solodovnikov A. S., “Geometriya prostranstv postoyannoi krivizny”, Itogi nauki i tekhn. Sovrem. problemy matematiki. Fundam. napravleniya, 29, 1980, 5–146

[28] Aminova A. V., “Psevdorimanovy mnogoobraziya s obschimi geodezicheskimi”, UMN, 48:2 (1993), 107–164 | MR | Zbl

[29] Aminova A. V., “Algebry Li infinitezimalnykh proektivnykh preobrazovanii lorentsevykh mnogoobrazii”, UMN, 50:1 (1995), 69–142 | MR | Zbl

[30] Aminova A. V., Proektivnye preobrazovaniya psevdorimanovykh mnogoobrazii, Yanus-K, M., 2002