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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2009, Volume 265, Pages 154–158
(Mi tm830)
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This article is cited in 1 scientific paper (total in 1 paper)
On a $p$-adic Wave Equation
A. N. Kochubei Institute of Mathematics, National Academy of Sciences of Ukraine, Kiev, Ukraine
Abstract:
It is shown that a "$p$-adic plane wave" $f(t+\omega_1x_1+\dots+\omega_nx_n)$, $(t,x_1,\dots,x_n)\in\mathbb Q_p^{n+1}$, where $f$ is a Bruhat–Schwartz complex-valued test function and $\max_{1\le j\le n}|\omega_j|_p=1$, satisfies, for any $f$, a certain homogeneous pseudodifferential equation, an analog of the classical wave equation. A theory of the Cauchy problem for this equation is developed.
Received in June 2008
Citation:
A. N. Kochubei, “On a $p$-adic Wave Equation”, Selected topics of mathematical physics and $p$-adic analysis, Collected papers, Trudy Mat. Inst. Steklova, 265, MAIK Nauka/Interperiodica, Moscow, 2009, 154–158; Proc. Steklov Inst. Math., 265 (2009), 143–147
Linking options:
https://www.mathnet.ru/eng/tm830 https://www.mathnet.ru/eng/tm/v265/p154
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Abstract page: | 367 | Full-text PDF : | 77 | References: | 70 |
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