Abstract
We study a boundary-value problem for a partial differential equation of parabolic type with coefficients in the form of Fourier series with coefficients and frequency slowly varying in time.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Yu. A. Mitropol'skii, G. P. Khoma, and M. I. Gromyak,Asymptotic Methods for Investigation of Quasiwave Equations of Hyperbolic Type [in Russian], Naukova Dumka, Kiev (1991).
A. M. Samoilenko and B. P. Tkach,Numerical-Analytic Methods in the Theory of Periodic Solutions of Partial Differential Equations [in Russian], Naukova Dumka, Kiev (1992).
A. V. Kostin and S. A. Shchegolev, “On a class of solutions of a differential system with slowly varying parameters,”Ukr. Mat. Zh.,41, No. 1, 101–103 (1989).
S. A. Shchegolev, “On solutions of a quasilinear differential system with periodic coefficients,”Ukr. Mat. Zh.,45, No. 8, 1157–1161 (1993).
A. N. Tikhonov and A. A. Samarskii,Equations of Mathematical Physics [in Russian], Nauka, Moscow (1980).
A. V. Kostin, “On the existence of particular solutions bounded or tending to zero ast → ∞ for a system of ordinary differential equations,”Differents. Uravn.,1, No. 5, 585–604 (1965).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 8, pp. 1129–1135, August, 1995.
Rights and permissions
About this article
Cite this article
Shchegolev, S.A. Construction of a solution of a quasilinear partial differential equation of parabolic type with oscillating and slowly varying coefficients. Ukr Math J 47, 1290–1298 (1995). https://doi.org/10.1007/BF01057717
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01057717