On a boundary value problem in a cylinder for a sixth-order pseudohyperbolic equation
Matematičeskie trudy, Tome 27 (2024) no. 3, pp. 30-51 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper considers the first boundary value problem in a cylinder for one sixth-order equation not resolved with respect to the highest derivative. Equation under study is a strictly pseudohyperbolic with lower terms. In this work, the existence and uniqueness of a generalized solution to a boundary value problem in an anisotropic Sobolev space is proved, and estimates for the solution are obtained.
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L. N. Bondar'; X. Ma. On a boundary value problem in a cylinder for a sixth-order pseudohyperbolic equation. Matematičeskie trudy, Tome 27 (2024) no. 3, pp. 30-51. http://geodesic.mathdoc.fr/item/MT_2024_27_3_a2/

[1] Demidenko G.V., Uspenskii S.V., Partial Differential Equations and Systems Not Solvable with Respect to the Highest-Order Derivative, Marcel Dekker, New York–Basel, 2003 | MR

[2] Pereira P. J. S., Lopes N. D., Trabuco L., “Soliton-type and other travelling wave solutions for an improved class of nonlinear sixth-order Boussinesq equations”, Nonlinear Dyn., 82 (2015), 783–818 | DOI | MR

[3] Umarov Kh. G., “Blow-up and global solvability of the Cauchy problem for a pseudohyperbolic equation related to the generalized Boussinesq equation”, Siberian Math. J., 63:3 (2022), 559–574 | DOI | MR

[4] Polat N., Piskin E., “Existence and asymptotic behavior of solution of Cauchy problem for the damped sixth-order Boussinesq equation”, Acta Math. Appl. Sin. Engl. Ser., 31 (2015), 735–746 | DOI | MR

[5] Wang S., Xue H., “Global solution for a generalized Boussinesq equation”, Appl. Math. Comput., 204:1 (2008), 130–136 | MR

[6] Ladyzhenskaya O. A., The boundary value problems of mathematical physics, Transl. from the Russian by Jack Lohwater, Applied Mathematical Sciences, 49, Springer-Verlag, New York etc., 1985, xxx+322 pp. (English) | DOI | MR

[7] Demidenko G. V., Sobolev Spaces and Generalized Solutions, Novosibirsk State University, Novosibirsk, 2015 (Russian)

[8] Mikhailov V. P., Partial differential equations, Mir, M., 1978 | MR

[9] Sobolev S. L., Introduction to the Theory of Cubature formulas, Nauka, M., 1974 (Russian)

[10] Trenogin V. A., Functional analysis, Fizmatlit, M., 2007 (Russian)

[11] Yosida K., Functional analysis, Springer-Verlag, Berlin–Heidelberg, 1995 (English) | MR

[12] Uspenskii S. V., Demidenko G. V., and Perepelkin V. G., Embedding Theorems and Applications to Differential Equations, Nauka, Novosibirsk, 1984 (Russian)