Partial differential equations/Numerical analysis
Cauchy problems with modified conditions for the Euler–Poisson–Darboux equations in the hyperbolic space
[Problèmes de Cauchy avec des conditions modifiées pour les équations dʼEuler–Poisson–Darboux dans lʼespace hyperbolique]
Comptes Rendus. Mathématique, Tome 351 (2013) no. 19-20, pp. 747-752.

On donne les solutions explicites des problèmes de Cauchy pour les équations dʼEuler–Poisson–Darboux, avec des conditions modifiées dans lʼespace hyperbolique avec application à lʼéquation des ondes.

In this note, we give the solutions of the Cauchy problems for the Euler–Poisson–Darboux equations (EPD) with modified conditions in the hyperbolic space with application to the wave equation.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.07.026
El-Hafedh, Cheikh Ould Mohamed 1 ; Telmoudy, Elbar Ould Ely 1 ; Ould Moustapha, Mohamed Vall 1

1 Unité de recherche “Analyse, EDP et modélisation”, faculté des sciences et techniques (FST), université des sciences, de technologie et de la medécine (USTM), B.P. 5026, Mauritania
@article{CRMATH_2013__351_19-20_747_0,
     author = {El-Hafedh, Cheikh Ould Mohamed and Telmoudy, Elbar Ould Ely and Ould Moustapha, Mohamed Vall},
     title = {Cauchy problems with modified conditions for the {Euler{\textendash}Poisson{\textendash}Darboux} equations in the hyperbolic space},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {747--752},
     publisher = {Elsevier},
     volume = {351},
     number = {19-20},
     year = {2013},
     doi = {10.1016/j.crma.2013.07.026},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2013.07.026/}
}
TY  - JOUR
AU  - El-Hafedh, Cheikh Ould Mohamed
AU  - Telmoudy, Elbar Ould Ely
AU  - Ould Moustapha, Mohamed Vall
TI  - Cauchy problems with modified conditions for the Euler–Poisson–Darboux equations in the hyperbolic space
JO  - Comptes Rendus. Mathématique
PY  - 2013
SP  - 747
EP  - 752
VL  - 351
IS  - 19-20
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2013.07.026/
DO  - 10.1016/j.crma.2013.07.026
LA  - en
ID  - CRMATH_2013__351_19-20_747_0
ER  - 
%0 Journal Article
%A El-Hafedh, Cheikh Ould Mohamed
%A Telmoudy, Elbar Ould Ely
%A Ould Moustapha, Mohamed Vall
%T Cauchy problems with modified conditions for the Euler–Poisson–Darboux equations in the hyperbolic space
%J Comptes Rendus. Mathématique
%D 2013
%P 747-752
%V 351
%N 19-20
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2013.07.026/
%R 10.1016/j.crma.2013.07.026
%G en
%F CRMATH_2013__351_19-20_747_0
El-Hafedh, Cheikh Ould Mohamed; Telmoudy, Elbar Ould Ely; Ould Moustapha, Mohamed Vall. Cauchy problems with modified conditions for the Euler–Poisson–Darboux equations in the hyperbolic space. Comptes Rendus. Mathématique, Tome 351 (2013) no. 19-20, pp. 747-752. doi : 10.1016/j.crma.2013.07.026. http://www.numdam.org/articles/10.1016/j.crma.2013.07.026/

[1] Bunke, Ulrich; Olbrich, Martin The wave kernel for the Laplacian on the classical locally symmetric spaces of rank one, theta functions, trace formulas and the Selberg zeta function, Ann. Glob. Anal. Geom., Volume 12 (1994), pp. 357-405

[2] El-hafedh, C.O.M.; Ould Moustapha, M.V. Problèmes de Cauchy avec des conditions modifiées pour les équations dʼEuler–Poisson–Darboux, C. R. Acad. Sci. Paris, Ser. I, Volume 349 (2011), pp. 1219-1224

[3] Intissar, A.; Ould Moustapha, M.V. Solution explicite de lʼéquation des ondes dans lʼespace symétrique de type non compact de rang 1, C. R. Acad. Sci. Paris, Ser. I, Volume 321 (1995), pp. 77-80

[4] Kipriyanov, I.A.; Ivanov, L.A. Euler–Poisson–Darboux equation on Riemannian space, Sov. Math. Dokl., Volume 260 (1981) no. 4, pp. 790-794

[5] Kipriyanov, I.A.; Ivanov, L.A. The Cauchy problem for the Euler–Poisson–Darboux equation in a homogeneous symmetric Riemannian space. I, Proc. Steklov Inst. Math., Volume 1 (1987), pp. 159-168

[6] Koornwinder, T.H. Jacobi functions and analysis on noncompact semisimple Lie groups (Askey, R.A.; Koornwinder, T.H.; Schempp, W., eds.), Special Functions: Group Theoretical Aspects and Applications, Reidel, Dordrecht, The Netherlands, 1984, pp. 1-85

[7] Lax, P.D.; Phillips, R.S. The asymptotic distribution of lattice points in Euclidean and non-Euclidean spaces, J. Funct. Anal., Volume 46 (1982), pp. 280-350

[8] Magnus, W.; Oberhettinger, F.; Soni, R.P. Formulas and Theorems for the Special Functions of Mathematical Physics, Springer-Verlag, New York, 1966

Cité par Sources :