EXISTENCE OF CLASSICAL WEAKENED SOLUTION ON THE AXIS OF THIRD CENTRALLY SYMMETRIC MIXED PROBLEM FOR SECOND ORDER HOMOGENEOUS THREE-DIMENSIONAL GENERAL HYPERBOLIC EQUATION
Keywords:
central symmetry’s wave, classical solution, a priori energetic inequality, d’Alembert’s method, Duhamel principleDOI:
https://doi.org/10.17654/0972111826001Abstract
We prove the existence of the classical weakened solution on the axis of the third mixed problem with central symmetry for the general homogeneous three-dimensional hyperbolic equation of the second order with minimal conditions on the initial data.
Received: July 12, 2025
Revised: August 17, 2025
Accepted: September 15, 2025
References
[1] Y. N. Ergorov, On the solution of the mixed boundary value problem for the vibration equation of a string, VESTNIK of Moscow State University, Series 1, Mathematics and Mechanics 5(3) (1961), 77-79.
[2] L. Hording, L. Hording, Cauchy Problem for Hyperbolic Equations, M. IL. (1961), 120.
[3] V. P. Ilhin and Y. I. Kuznestov, Algebraic Foundations of Numerical Analysis, Naouka Edition, 1986, p. 184.
[4] F. E. Lomocev and N. I. Yurtchuk, Cauchy problem for hyperbolic equation of second order differential operators, Differential Equation 12(12) (1976), 2242-2250.
[5] I. G. Petrowsky, Course on Partial Differential Equations, Moscow, Fizmatgiz, 1961, p. 400.
[6] Y. V. Radino and N. I. Yurtchuk, Cauchy problem for certain abstract hyperbolic equations of even order, Differential Equations 12(2) (1976), 331-342.
[7] P. K. Siliadin, N. Gbenouga and K. Tcharie, On the existence and uniqueness of classical solution of mixed problem for general equation of a wave with central symmetry, Advances in Differential Equations and Control Processes 23(2) (2020), 205-220.
[8] P. K. Siliadin and K. Tcharie, Sur la nature de l’équation générale d’une onde du second ordre à symétrie centrale, J. Rech. Sci. Univ. Lomé (Togo) 21(1) (2019), 175-181.
[9] V. I. Smirnov, Course in higher mathematics, T.IV.M.-L: State Editions of Technical and Theoretical Literature, 1951, p. 804.
[10] K. Tcharie, On the Classical Solution of the First Mixed Problem for the One-dimensional Hyperbolic Equation of Even Order, Thesis, Belarusian State University, MINSK 1993.
[11] V. A. Tchernyatin, On the precision of the theorem on the existence of the classical solution of the mixed problem for a one-dimensional wave equation, Equations Différentielles (CEI) 21(9) (1985), 1569-1576.
[12] A. N. Tikhanov and A. A. Samarsky, Équation of Mathematical Physics, M. Naouka, 1972, p. 735.
[13] V. I. Yashkin and N. I. Yurtchuk, On the classical solution of mixed problems with wave operators in the case of central symmetry, Thesis 1991, Belarusian State University, 1991, p. 84.
[14] N. I. Yurtchuk, V. I. Yashkin and K. Tcharie, A classical solution, weakened on the axis of a centrally symmetric mixed problem for a tree dimensional hyperbolic equation in Hölder spaces, J. Rech. Sci. Belarus. 37(6) (1999), 844-846.
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