Well-posedness of the Dirichlet and Poincaré problems for a multidimensional Gellerstedt equation in a cylindrical domain
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We prove the unique solvability of the Dirichlet and Poincaré problems for a multidimensional Gellerstedt equation in a cylindrical domain. We also obtain a criterion for the unique solvability of these problems.
KeywordsCauchy Problem Dirichlet Problem Hyperbolic Equation Spherical Function Homogeneous Problem
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- 2.A. V. Bitsadze, Equations of the Mixed Type [in Russian], Academy of Sciences of the USSR, Moscow (1959).Google Scholar
- 3.A. M. Nakhushev, Problems with Displacement for Partial Differential Equation [in Russian], Nauka, Moscow (2006).Google Scholar
- 7.D. R. Dunninger and E. C. Zachmanoglou, “The condition for uniqueness of the Dirichlet problem for hyperbolic equations in cylindrical domains,” J. Math. Mech., 18, No. 8 (1969).Google Scholar
- 8.S. A. Aldashev, “The well-posedness of the Dirichlet problem in the cylindrical domain for the multidimensional wave equation,” Math. Probl. Eng., 2010, Article ID 653215 (2010).Google Scholar
- 10.S. G. Mikhlin, Multidimensional Singular Integrals and Integral Equations [in Russian], Fizmatgiz, Moscow (1962).Google Scholar
- 11.S. A. Aldashev, Boundary-Value Problems for Multidimensional Hyperbolic and Mixed Equations [in Russian], Gylym, Alma-Ata (1994).Google Scholar
- 12.V. A. Tersenov, Introduction to the Theory of Equations Degenerating on the Boundary [in Russian], Novosibirsk State University, Novosibirsk (1973).Google Scholar
- 13.A. M. Nakhushev, Equations of Mathematical Biology [in Russian], Vysshaya Shkola, Moscow (1985).Google Scholar
- 14.H. Bateman and A. Erdélyi, Higher Transcendental Functions, Vol. 2, McGraw-Hill, New York (1954).Google Scholar
- 15.A. N. Tikhonov and A. A. Samarskii, Equations of Mathematical Physics [in Russian], Nauka, Moscow (1966).Google Scholar
- 16.S. A. Aldashev and R. B. Selikhanova, “On Darboux problems with deviation from a characteristic and related problems for degenerate multidimensional hyperbolic equations,” Dokl. Adyg. (Cherkessk.) Mezhd. Akad. Nauk, 9, No. 2, 24–27 (2007).Google Scholar