Asymptotic solution of the Cauchy problem for the singularly perturbed partial integro-differential equation with rapidly oscillating coefficients and with rapidly oscillating heterogeneity
Kalimbetov B.T. Tuychiev O.D.
1 January 2021De Gruyter Open Ltd
Open Mathematics
2021#19Issue 1244 - 258 pp.
In this paper, the regularization method of S. A. Lomov is generalized to integro-differential equations with rapidly oscillating coefficients and with a rapidly oscillating right-hand side. The main goal of the work is to reveal the influence of the oscillating components on the structure of the asymptotics of the solution of this problem. The case of coincidence of the frequencies of a rapidly oscillating coefficient and a rapidly oscillating inhomogeneity is considered. In this case, only the identical resonance is observed in the problem. Other cases of the relationship between frequencies can lead to so-called non-identical resonances, the study of which is nontrivial and requires the development of a new approach. It is supposed to study these cases in our further work.
integro-partial differential equation , iterative problems , regularization of an integral , singularly perturbed , solvability of iterative problems , space of non-resonant solutions
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Akhmed Yassawi University, B. Sattarkhanov 29, Turkestan, 161200, Kazakhstan
Khudjant State University Named after B. Gafurov, Movlonbekov Ave., Khudjant, 735700, Tajikistan
Akhmed Yassawi University
Khudjant State University Named after B. Gafurov
10 лет помогаем публиковать статьи Международный издатель
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