Criterion for the Uniqueness of the Regular Solution of the Dirichlet and Poincare Problems for the Multi-Dimensional Euler~--- Darboux~--- Poisson Equation
Dalʹnevostočnyj matematičeskij žurnal, Tome 12 (2012) no. 2, pp. 127-135.

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

This paper establishes the criterion for the uniqueness of the regular solution of the Dirichlet and Poincare problems in a cylindrical domain for the multi-dimensional Euler — Darboux — Poisson equation.
@article{DVMG_2012_12_2_a0,
     author = {S. A. Aldashev},
     title = {Criterion for the {Uniqueness} of the {Regular} {Solution} of the {Dirichlet} and {Poincare} {Problems}  for the {Multi-Dimensional} {Euler~---} {Darboux~---} {Poisson} {Equation}},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {127--135},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2012_12_2_a0/}
}
TY  - JOUR
AU  - S. A. Aldashev
TI  - Criterion for the Uniqueness of the Regular Solution of the Dirichlet and Poincare Problems  for the Multi-Dimensional Euler~--- Darboux~--- Poisson Equation
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2012
SP  - 127
EP  - 135
VL  - 12
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DVMG_2012_12_2_a0/
LA  - ru
ID  - DVMG_2012_12_2_a0
ER  - 
%0 Journal Article
%A S. A. Aldashev
%T Criterion for the Uniqueness of the Regular Solution of the Dirichlet and Poincare Problems  for the Multi-Dimensional Euler~--- Darboux~--- Poisson Equation
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2012
%P 127-135
%V 12
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DVMG_2012_12_2_a0/
%G ru
%F DVMG_2012_12_2_a0
S. A. Aldashev. Criterion for the Uniqueness of the Regular Solution of the Dirichlet and Poincare Problems  for the Multi-Dimensional Euler~--- Darboux~--- Poisson Equation. Dalʹnevostočnyj matematičeskij žurnal, Tome 12 (2012) no. 2, pp. 127-135. http://geodesic.mathdoc.fr/item/DVMG_2012_12_2_a0/

[1] J. Hadamard, “Sur les problemes aux derivees partielles et leur signification physique”, Princeton University Bulletin, 13 (1902), 49–52 | MR

[2] A. V. Bitsadze, Uravneniya smeshannogo tipa, AN SSSR, M., 1959, 164 pp.

[3] A. M. Nakhushev, Zadachi so smescheniem dlya uravneniya v chastnykh proizvodnykh, Nauka, M., 2006, 287 pp.

[4] D. G. Bourgin and R. Duffin, “The Dirichlet problem the vibrating string eguation”, Bulletin of the American Mathematical Society, 45 (1939), 851–858 | DOI | MR

[5] D. W. Fox and C. Pucci, “The Dirichlet problem the wave eguation”, Annali di Mathematica Pura ed Applicata, 46 (1958), 155–182 | DOI | MR | Zbl

[6] A. M. Nakhushev, “Kriterii edinstvennosti zadachi Dirikhle dlya uravneniya smeshannogo tipa v tsilindricheskoi oblasti”, Differentsialnye uravneniya, 6:1 (1970), 190–191 | Zbl

[7] D. R. Dunninger, E. C. Zachmanoglou, “The condition for uniqueness of the Diriclet problem for hyperbolic equations in cilindrical domains”, J. Math. Mech., 18:8 (1969), 763–766 | MR | Zbl

[8] S. A. Aldashev, “The well-posedness of the Dirichlet problem in the cylindric domain for the multidimensional wave equation”, Article ID 653215, Mathematical problems Engineering, 2010 (2010), 1–7 | DOI | MR

[9] S. A. Aldashev, “Korrektnost zadachi Puankare v tsilindricheskoi oblasti dlya mnogomernogo volnovogo uravneniya”, Sovremennaya matematika i ee prilozheniya, 67, Uravneniya s chastnymi proizvodnymi (2010), 28–32 | MR

[10] S. G. Mikhlin, Mnogomernye singulyarnye integraly i integralnye uravneniya, Fizmatgiz, M., 1962, 254 pp. | MR | Zbl

[11] S. A. Aldashev, Kraevye zadachi dlya mnogomernykh giperbolicheskikh i smeshannykh uravnenii, Gylym, Almaty, 1994, 170 pp.

[12] E. T. Copson, “On the Riemann — Green function”, J. Rath. Mech and Anal., 1 (1958), 324–348 | DOI | MR | Zbl

[13] A. Weinstein, “On the wave equation and the equation of Euler — Poisson”, The Fifth simposium in applied Math., MCGraw-Hill, New York, 1954, 137–147 | DOI | MR

[14] S. A. Tersenov, Vvedenie v teoriyu uravnenii, vyrozhdayuschikhsya na granitse, NGU, Novosibirsk, 1973, 144 pp. | MR

[15] S. A. Aldashev, “O nekotorykh kraevykh zadachakh dlya odnogo klassa singulyarnykh uravnenii v chastnykh proizvodnykh”, Differents. uravneniya, 12:6 (1976), 3–14 | Zbl

[16] S. A. Tersenov, Vvedenie v teoriyu uravnenii parabolicheskogo tipa s menyayuschimsya napravleniem vremeni, IM SOAN SSSR, Novosibirsk, 1982, 167 pp. | MR

[17] A. M. Nakhushev, Elementy drobnogo ischesleniya i ikh primenenie, KBNTs RAN, Nalchik, 2000, 298 pp.