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This article is cited in 5 scientific papers (total in 5 papers)
On the behaviour for large values of the time of the solution of the Cauchy problem for the equation $\frac{\partial^2u}{\partial t^2}-\frac{\partial^2u}{\partial x^2}+\alpha(x)u=0$
S. A. Laptev
Abstract:
We obtain an asymptotic expansion as $t\to\infty$ for the solution $u(t,x)$ of the Cauchy problem with initial functions of compact support for the equation
$$
u_{tt}-u_{xx}+(\alpha_0+\varphi(x))u=0,\qquad t>0,\quad-\infty<x<\infty,
$$
where $\alpha_0=\text{const}$ and $\varphi(x)$ satisfies the following condition for some $k\geqslant1$:
$$
\int_{-\infty}^\infty|x|^k|\varphi(x)|\,dx<\infty.
$$
Bibliography: 4 titles.
Received: 20.02.1975
Citation:
S. A. Laptev, “On the behaviour for large values of the time of the solution of the Cauchy problem for the equation $\frac{\partial^2u}{\partial t^2}-\frac{\partial^2u}{\partial x^2}+\alpha(x)u=0$”, Math. USSR-Sb., 26:3 (1975), 403–426
Linking options:
https://www.mathnet.ru/eng/sm3660https://doi.org/10.1070/SM1975v026n03ABEH002488 https://www.mathnet.ru/eng/sm/v139/i3/p435
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Abstract page: | 266 | Russian version PDF: | 111 | English version PDF: | 12 | References: | 47 |
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