We study the problem of existence and uniqueness of the solution of a mixed problem for the Petrovskii well-posed equation in a cylindrical domain and the behavior of this solution for large values of time.
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S. S. Voit, “Propagation of initial condensations in viscous gases,” Uchen. Zap. MGU, Ser. Mekh., 5, No. 172, 125–142 (1954).
M. L. Gorbachuk, A. N. Kochubei, and A. Ya. Shklyar, “On the stabilization of solutions of differential equations in Hilbert spaces,” Dokl. Ros. Akad. Nauk, 341, No. 6, 734–736 (1995).
B. A. Iskenderov and E. S. Huseynova, “On a mixed problem in boundary domain for one equation correct by Petrovskii and estimate of its solution,” Trans. NAS Azerbaijan, Ser. Phys.-Techn., Math. Sci., 25, No. 7, 31–40 (2005).
E. S. Huseynova, “On a behavior of the solution of Cauchy problem for one correct by Petrovsky equation at large time,” Trans. NAS Azerbaijan, Ser. Phys.-Techn., Math. Sci., 26, No. 7, 85–96 (2006).
V. S. Vladimirov, Equations of Mathematical Physics [in Russian], Nauka, Moscow (1981).
V. I. Smirnov, A Course of Higher Mathematics [in Russian], Vol. 5, Fizmatgiz, Moscow (1953).
S. Mizohata, The Theory of Partial Differential Equations, Cambridge University, New York (1977).
B. A. Iskenderov, “Principles of radiation for elliptic equation in the cylindrical domain,” in: Colloq. Math. Sic. Janos Bolyai, Szeged, Hungary (1988), pp. 249–261.
A. F. Nikiforov and V. B. Uvarov, Foundations of the Theory of Special Functions [in Russian], Nauka, Moscow (1974).
V. P. Mikhailov, Partial Differential Equations [in Russian], Nauka, Moscow (1983).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 2, pp. 214–230, February, 2009.
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Iskenderov, B.A., Guseinova, É.S. Mixed problem for the Petrovskii well-posed equation in a cylindrical domain. Ukr Math J 61, 259–276 (2009). https://doi.org/10.1007/s11253-009-0208-y
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DOI: https://doi.org/10.1007/s11253-009-0208-y