2019
Том 71
№ 11

All Issues

Boundary-Value Problem for Weakly Nonlinear Hyperbolic Equations with Variable Coefficients

Bilusyak N.I., Ptashnik B. I.

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Abstract

We establish conditions for the unique solvability of a boundary-value problem for a weakly nonlinear hyperbolic equation of order 2n, n > (3p + 1)/2, with coefficients dependent on the space coordinates and data given on the entire boundary of a cylindric domain \(D \subset \mathbb{R}^{p + 1}\) . The investigation of this problem is connected with the problem of small denominators.

English version (Springer): Ukrainian Mathematical Journal 53 (2001), no. 9, pp 1546-1553.

Citation Example: Bilusyak N.I., Ptashnik B. I. Boundary-Value Problem for Weakly Nonlinear Hyperbolic Equations with Variable Coefficients // Ukr. Mat. Zh. - 2001. - 53, № 9. - pp. 1281-1286.

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