Geodesic
Representations for the solutions and coefficients of evolution equations
Sibirskij žurnal industrialʹnoj matematiki, Tome 16 (2013) no. 2, pp. 40-49.

Voir la notice de l'article provenant de la source Math-Net.Ru

We give new representations for the solutions and coefficients of evolution equations in the linear case. The obtained formulas contain functional arbitrariness, which can be used in identification problems. We also give classes of hyperbolic equations admitting generalized functional-invariant solutions.
Keywords: second-order evolution differential equations, generalized functional-invariant solutions.
Mots-clés : Poisson formula 
@article{SJIM_2013_16_2_a3,
     author = {Yu. E. Anikonov and M. V. Neshchadim},
     title = {Representations for the solutions and coefficients of evolution equations},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {40--49},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2013_16_2_a3/}
}
TY  - JOUR
AU  - Yu. E. Anikonov
AU  - M. V. Neshchadim
TI  - Representations for the solutions and coefficients of evolution equations
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2013
SP  - 40
EP  - 49
VL  - 16
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2013_16_2_a3/
LA  - ru
ID  - SJIM_2013_16_2_a3
ER  - 
%0 Journal Article
%A Yu. E. Anikonov
%A M. V. Neshchadim
%T Representations for the solutions and coefficients of evolution equations
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2013
%P 40-49
%V 16
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2013_16_2_a3/
%G ru
%F SJIM_2013_16_2_a3
Yu. E. Anikonov; M. V. Neshchadim. Representations for the solutions and coefficients of evolution equations. Sibirskij žurnal industrialʹnoj matematiki, Tome 16 (2013) no. 2, pp. 40-49. http://geodesic.mathdoc.fr/item/SJIM_2013_16_2_a3/

[1] Anikonov Yu. E., Neschadim M. V., “Predstavleniya dlya reshenii i koeffitsientov differentsialnykh uravnenii 2-go poryadka”, Sib. zhurn. industr. matematiki, 15:4(52) (2012), 17–23

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

[3] Smirnov V. I., Sobolev S. L., Novyi metod resheniya ploskoi zadachi uprugikh kolebanii, Trudy Seismolog. in-ta AN SSSR, 20, Izd-vo AN SSSR, L., 1932, 37 pp.

[4] Sobolev S. L., “Funktsionalno-invariantnye resheniya volnovogo uravneniya”, Trudy Fiz.-mat. in-ta im. Steklova, 5, 1934, 259–264 | Zbl

[5] Erugin N. P., Smirnov M. M., “Funktsionalno-invariantnye resheniya differentsialnykh uravnenii”, Differents. uravneniya, 17:5 (1981), 853–865 | MR | Zbl

[6] Menshikh O. F., “O funktsionalno-invariantnykh resheniyakh kvazilineinykh uravnenii s chastnymi proizvodnymi vtorogo poryadka”, Differents. uravneniya, 11:3 (1975), 531–540

[7] Kiselev A. P., Perel M. V., “Otnositelno neiskazhayuschiesya volny dlya $m$-mernogo volnovogo uravneniya”, Differents. uravneniya, 38:8 (2002), 1128–1129 | MR | Zbl

[8] Ovsyannikov L. V., “Dvoinye zvukovye volny”, Sib. mat. zhurn., 36:3 (1995), 611–618 | MR | Zbl

[9] Finikov S. P., Metod vneshnikh form Kartana, Gostekhizdat, M.–L., 1948

[10] Romanov V. G., Ustoichivost v obratnykh zadachakh, Nauch. mir, M., 2005 | MR

[11] Anikonov Yu. E., Formulas in Inverse and Ill-Posed Problems, VSP, Utrecht, 1997 | MR | Zbl

[12] Gelfand I. M., Shilov G. E., Obobschennye funktsii i deistviya nad nimi, Dobrosvet, M., 2000

[13] Riordan Dzh., Vvedenie v kombinatornyi analiz, Izd-vo inostr. lit., M., 1963