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This article is cited in 6 scientific papers (total in 6 papers)
Integro-differential equation of non-local wave interaction
N. B. Engibaryan, A. Kh. Khachatryan Institute of Mathematics, National Academy of Sciences of Armenia
Abstract:
The integro-differential equation
$$
\frac{d^2f}{dx^2}+Af=\int^\infty_0K(x-t)f(t)\,dt+g(x)
$$
with kernel
$$
K(x)=\lambda\int^\infty_ae^{-|x|p}G(p)\,dp, \qquad a\geqslant0,
$$
is considered, in which
$$
A>0,\qquad \lambda\in(-\infty,\infty), \qquad G(p)\geqslant0,
\qquad 2\int^\infty_a\frac1p\,G(p)\,dp=1.
$$
These equations arise, in particular, in the theory of non-local wave interaction. A factorization method of their analysis and solution is developed.
Bibliography: 9 titles.
Received: 19.12.2003 and 12.03.2007
Citation:
N. B. Engibaryan, A. Kh. Khachatryan, “Integro-differential equation of non-local wave interaction”, Mat. Sb., 198:6 (2007), 89–106; Sb. Math., 198:6 (2007), 839–855
Linking options:
https://www.mathnet.ru/eng/sm3826https://doi.org/10.1070/SM2007v198n06ABEH003863 https://www.mathnet.ru/eng/sm/v198/i6/p89
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Abstract page: | 657 | Russian version PDF: | 190 | English version PDF: | 3 | References: | 48 | First page: | 11 |
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