Existence, uniqueness, and dependence on a parameter of solutions of differential-functional equations with ordinary and partial derivatives
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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.
KeywordsCauchy Problem Average Method Successive Approximation Hyperbolic System Initial Function
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- 1.Yu. A. Mitropol’skii and B. I. Moseenkov, Asymptotic Solutions of Partial Differential Equations [in Russian], Vyshcha Shkola, Kiev (1976).Google Scholar
- 2.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).Google Scholar
- 3.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).Google Scholar
- 5.V. P. Rubanik, Oscillations of Complex Quasilinear Systems with Lag [in Russian], Universitetskoe, Minsk (1985).Google Scholar
- 6.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.Google Scholar
- 7.I. G. Petrovski, Lectures on Partial Differential Equations [in Russian], Fizmatgiz, Moscow (1961).Google Scholar
- 8.Yu. A. Mitropol’skii, Averaging Method in Nonlinear Mechanics [in Russian], Naukova Dumka, Kiev (1971).Google Scholar