Temporary deformations of degrees of the wave operator
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 34, Tome 324 (2005), pp. 213-228 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The conditions at which the linear differential operators of the second order are equivalent to operators not containing of “friction” (first partial derivatives) are investigated. One can construct iso-Huygens deformations for degrees of the wave operator with time-dependent coefficients. The fundamental solutions of these deformations and conditions, at which the Huygens principle holds are found.
@article{ZNSL_2005_324_a12,
     author = {S. P. Khekalo},
     title = {Temporary deformations of degrees of the wave operator},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {213--228},
     year = {2005},
     volume = {324},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2005_324_a12/}
}
TY  - JOUR
AU  - S. P. Khekalo
TI  - Temporary deformations of degrees of the wave operator
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2005
SP  - 213
EP  - 228
VL  - 324
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2005_324_a12/
LA  - ru
ID  - ZNSL_2005_324_a12
ER  - 
%0 Journal Article
%A S. P. Khekalo
%T Temporary deformations of degrees of the wave operator
%J Zapiski Nauchnykh Seminarov POMI
%D 2005
%P 213-228
%V 324
%U http://geodesic.mathdoc.fr/item/ZNSL_2005_324_a12/
%G ru
%F ZNSL_2005_324_a12
S. P. Khekalo. Temporary deformations of degrees of the wave operator. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 34, Tome 324 (2005), pp. 213-228. http://geodesic.mathdoc.fr/item/ZNSL_2005_324_a12/

[1] M. Riesz, “L'integrale de Riemann-Liouville et le probleme de Cauchi”, Acta Math., 81 (1949), 1–223 | DOI | MR | Zbl

[2] Y. Berest, Y. Molchanov, “Fundamental solution for partial differential equations with reflection group invariance”, J. Math. Phis., 36:8 (1995), 4324–4339 | DOI | MR | Zbl

[3] Yu. Yu. Berest, A. P. Veselov, “Printsip Gyuigensa i integriruemost”, UMN, 49:6(300) (1994), 8–78 | MR

[4] N. Kh. Ibragimov, A. O. Oganesyan, “Ierarkhiya gyuigensovykh uravnenii v prostranstvakh s netrivialnoi konformnoi gruppoi”, UMN, 46:3(278) (1991), 111–146 | MR | Zbl

[5] S. P. Khekalo, “Izogyuigensovy deformatsii ultragiperbolicheskogo operatora”, Zap. nauchn. semin. POMI, 285, 2002, 207–223 | MR | Zbl

[6] V. M. Babich, “Anzatts Adamara, ego analogi, obobscheniya, prilozheniya”, Algebra i analiz, 3:5 (1991), 1–37 | MR

[7] Y. Berest, “Hierarchies of Huygens' Operators and Hadamard's Conjecture”, Acta Appl. Math., 53 (1998), 125–185 | DOI | MR | Zbl

[8] V. I. Semyanistyi, “Nekotorye zadachi integralnoi geometrii v psevdoevklidovykh i neevklidovykh prostranstvakh”, MGU, Trudy sem. po vekt. i tenz. an., 13 (1963), 244–302

[9] B. Rubin, Zeta integrals and integral geometry in the spase of rectangular matrices, Preprint, The Hebrew Univ. of Jerusalem, 2004, 1–49 | MR

[10] I. M. Gelfand, S. G. Gindikin, M. I. Graev, Izbrannye zadachi integralnoi geometrii, Dobrosvet, M., 2000 | MR

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

[12] E. Cotton, “Sur les invariants differentieles de quelques equations lineaires aux de rivees partielles du second ordre”, Ann. Sci. Ecole Norm. Sup., 17 (1900), 211–244 | MR | Zbl

[13] V. A. Zorich, Matematicheskii analiz, T. 2, Nauka, M., 1984 | MR

[14] I. M. Gelfand, G. E. Shilov, Obobschennye funktsii i deistviya nad nimi, Vyp. 1, Fizmatgiz, M., 1985

[15] Zh. Trev, Lektsii po lineinym uravneniyam v chastnykh proizvodnykh s postoyannymi koeffitsientami, Mir, M., 1965 | Zbl

[16] S. P. Khekalo, “Kalibrovochno ekvivalentnye deformatsii obyknovennykh lineinykh differentsialnykh operatorov s postoyannymi koeffitsientami”, Zap. nauchn. semin. POMI, 308, 2004, 235–251 | MR | Zbl

[17] J. E. Lagnese, K. L. Stellmacher, “A method of generating classes of Huygens' operators”, J. Math. Mech., 17:5 (1967), 461–472 | MR | Zbl