КРИТЕРИЙ ОДНОЗНАЧНОЙ РАЗРЕШИМОСТИ СПЕКТРАЛЬНЫХ ЗАДАЧ ДИРИХЛЕ И ПУАНКАРЕ ДЛЯ МНОГОМЕРНОГО УРАВНЕНИЯ ЭЙЛЕРА - ДАРБУ - ПУАССОНА
DOI:
https://doi.org/10.18413/2687-0959-2020-52-2-139-145Ключевые слова:
критерий, спектральные задачи, многомерное уравпепие, цилиндрическая область, функция БесселяАннотация
В цилиндрической области евклидова пространства для многомерного уравпепия Эйлера - Дарбу — Пуассона рассматриваются спектральные задачи Дирихле и Пуанкаре. Решение ищется в виде разложения по многомерным сферическим функциям. Доказаны теоремы существования и едипствеппо- сти классического решепия. Получены условия однозначной разрешимости поставленных задач, которые существенно зависят от высоты цилиндра.
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Библиографические ссылки
Aldashev S. A. 2003. Spectral Darboux-Protter problems for a class of multidimensional hyperbolic equations. Ukr. Mat. Zh., 55(1): 100-108 (in Russian).
Aldashev S. A. 2005. Criterion for the existence of eigenfunctions of the Darboux-Protter spectral problem for degenerate multidimensional hyperbolic equations. Diff. equat., 411(6): 795-801 (in Russian).
Aldashev S. A. 2006. Criterion for the existence of eigenfunctions of Darboux-Protter spectral problems for the multidimensional Euler-Darboux-Poisson equation. Izv.vuzov.Matem., 2: 3-10 (in Russian).
Aldashev S. A. 2014. Criterion for unambiguous solvability of the Dirichlet spectral problem in a cylindrical domain for multidimensional hyperbolic equations with a wave operator. Samara., Vestnik SamGTU, ser. fiz-mat sciences, 3(36): 21-30 (in Russian).
Aldashev S. A. 2010. Criterion of volterrity of the Dirichlet spectral problem in a cylindrical domain for a multidimensional wave equation. Almaty., Izvestiya NAN RK, ser.fiz-mat. sciences, 1(269): 3-5 (in Russian).
Aldashev S. A. 2011. Criterion of unambiguous solvability of the Poincare spectral problem in a cylindrical domain for a multidimensional wave equation. Materials of the I-international conference of young scientists «Math, modeling of fractal processes, related problems of analysis and computer science». Nalchik., Institute PMA KBSC Russian Academy of Sciences, 33-39 (in Russian).
Aldashev S. A. 1991. Boundary value problems for multidimensional hyperbolic and mixed equations, Almaty., Gylym, 170 (in Russian).
Aldashev S. A. 1976. On some boundary value problems for a class of singular partial differential equations. Diffcrcnts.equations, 12(6): 3-14 (in Russian).
Kalmcnov T. Sh. 1993. Boundary value problems for linear partial differential equations of hyperbolic type Shymkent-., Gylym, 32 (in Russian).
Copson E.T. 1958. On the Riemann-Green function. J.Rath Meeh and Anal., 1: 324-348.
Mikhlin S. G. 1962. Multidimensional singular integrals and integral equations, M., Fizmatgiz, 254 (in Russian).
Moiseev E. N. 1988. Equation of mixed type with spectral parameters M., MGU, 150 (in Russian).
Nakhushev A. M. 2006. Problems with displacement for partial differential equations, M., Nauka, 287 (in Russian).
Nakhushev A. M., 2000. The Elements of fractional calculus and their applications, Nalchik., KBSC RAN, 298 (in Russian).
Sabitov К. B., Ilyasov R. R. 2000. On the incorrectness of boundary value problems for a class of hyperbolic equations. Izv.vuzov.Math., 5.: 59-60 (in Russian).
Tersenov S. A. 1973. Introduction to the theory of equations degenerating on the boundary, Novosibirsk., NGU, 144 (in Russian).
Tersenov S. A. 1982. Introduction to the theory of parabolic type equations with a changing direction of time, Novosibirsk., IM SOAN USSR, 167 (in Russian).
He K. Ch. 2000. On eigenfunctions of homogeneous boundary value problems for an elliptic equation with Bessel operators. Non-classical equations of mathematical physics. Novosibirsk. IM SO RAN, 128=-135 (in Russian).
Weinstein A. 1954. On the wave equation and the equation of Euler-Poisson. The Fifth symposium in applied Math. MC Graw-Hill, New York, 137-147.
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