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This article is cited in 4 scientific papers (total in 4 papers)
On uniform quasiasymptotics of solutions of the second mixed problem for a hyperbolic equation
A. K. Gushchin, V. P. Mikhailov
Abstract:
This paper is devoted to the study of uniform quasiasymptotics of the solution of the second mixed problem in $(0,+\infty)\times\Omega$, $\Omega\in\mathbf R_n$, and of the Cauchy problem $(\Omega=\mathbf R_n)$ for the linear hyperbolic equation
$$
u_{tt}-\sum_{i,j=1}^n(a_{ij}(x)u_{x_i})_{x_j}=f(t,x)
$$
with initial conditions
$$
u|_{t=0}=\varphi(x),\qquad u_t|_{t=0}=\psi(x).
$$
A criterion for the existence of quasiasymptotics of the solution of order $\alpha+2$ is established under the assumption that the function $F(t,x)=f(t,x)\theta(t)+\psi(x)\delta(t)+\varphi(x)\delta'(t)$ has quasiasymptotics of order $\alpha$ and with a certain condition of “isoperimetric type” on the class of domains $\Omega$ considered.
Bibliography: 13 titles.
Received: 21.04.1986
Citation:
A. K. Gushchin, V. P. Mikhailov, “On uniform quasiasymptotics of solutions of the second mixed problem for a hyperbolic equation”, Mat. Sb. (N.S.), 131(173):4(12) (1986), 419–437; Math. USSR-Sb., 59:2 (1988), 409–427
Linking options:
https://www.mathnet.ru/eng/sm1971https://doi.org/10.1070/SM1988v059n02ABEH003144 https://www.mathnet.ru/eng/sm/v173/i4/p419
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Abstract page: | 455 | Russian version PDF: | 113 | English version PDF: | 11 | References: | 80 | First page: | 3 |
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