Abstract
For a system of quasilinear hyperbolic equations with a system of differential equations with lag, we prove theorems on the existence and uniqueness of a solution of the Cauchy problem and its continuous dependence on the initial conditions.
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References
Yu. A. Mitropol’skii and B. I. Moseenkov, Asymptotic Solutions of Partial Differential Equations [in Russian], Vyshcha Shkola, Kiev (1976).
M. I. Rabinovich and A. A. Rosenblyum, “On a justification of asymptotic methods in the theory of oscillations of distributed systems”, Dokl. Akad. Nauk SSSR, 199, No. 3, 575–578 (1971).
V. A. Dombrovskii and G. P. Khoma, “Averaging theorems for hyperbolic systems of the first order with retarded argument,” Mat. Fizika, No. 10, 134–141 (1971).
G. P. Khoma, “Averaging in hyperbolic systems of standard kind with retarded argument,” Ukr. Mat. Zh., 30, No. 9, 133–135 (1978).
V. P. Rubanik, Oscillations of Complex Quasilinear Systems with Lag [in Russian], Universitetskoe, Minsk (1985).
Ya. I. Bigun, “On the well-posedness and the averaging method in the system of hyperbolic equations and differential equations with lag,” in: Systems of Evolutionary Equations with Aftereffect [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences Kiev (1994), pp. 4–17.
I. G. Petrovski, Lectures on Partial Differential Equations [in Russian], Fizmatgiz, Moscow (1961).
Yu. A. Mitropol’skii, Averaging Method in Nonlinear Mechanics [in Russian], Naukova Dumka, Kiev (1971).
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 5, pp. 715–719, May, 1997.
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Bigun, Y.I. Existence, uniqueness, and dependence on a parameter of solutions of differential-functional equations with ordinary and partial derivatives. Ukr Math J 49, 798–804 (1997). https://doi.org/10.1007/BF02486461
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DOI: https://doi.org/10.1007/BF02486461