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$L^2$-theory of singular perturbation of hyperbolic equations III Asymptotic expansions of dispersive type
http://hdl.handle.net/2261/1541
http://hdl.handle.net/2261/15415f2233b1-f563-47fa-bb4f-a98f39a3e5f9
名前 / ファイル | ライセンス | アクション |
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jms030110.pdf (313.6 kB)
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Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
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公開日 | 2008-03-04 | |||||
タイトル | ||||||
タイトル | $L^2$-theory of singular perturbation of hyperbolic equations III Asymptotic expansions of dispersive type | |||||
言語 | ||||||
言語 | eng | |||||
資源タイプ | ||||||
資源 | http://purl.org/coar/resource_type/c_6501 | |||||
タイプ | departmental bulletin paper | |||||
著者 |
Uchiyama, Koichi
× Uchiyama, Koichi |
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抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | We consider Cauchy problems for linear strictly hyperbolic equations of order $l$ with a small parameter $ε \in (0, ε_0 ]$ : % \begin{eqnarray} &\{ &\hspace{-3mm} (i ε )^{l-m} L (t,x,D_t , D_x; ε)+ M(t,x,D_t , D_x ;ε) \} u(t,x; ε) \\ && =f(t,x;ε) \ onumber \\ &&\mbox{for} (t,x) \in (0,T) × \mbox{\boldmath $R$ }_x^d, \ onumber \end{eqnarray} % \begin{equation} D_t^j u(0,x; ε ) = g_j (x;ε) j=0,1,2, \ldots, l-1 \label{eqn: 0.2} \end{equation} % where $L$ and $M$ are linear strictly hyperbolic operators of order $l$ and $m$ \((l = m+1\) or $m+2$) with $C^\infty$ bounded derivatives with respect to \((t,x,ε) \in [0,\infty) × \mbox{\boldmath $R$ }^d × [0,ε_0]\). The aim of this paper is to give \(C^{\infty}\) asymptotic expansions of solutions to singularly perturbed Cauchy problems of this type, when the characteristic roots of $L$ and $M$ satisfy the separation conditions. The points are to construct formal solutions (Proposition 5.3, 5.4), consisting of the regular part and the singular one (correction part of dispersive type) expressed by Maslov's canonical operators, and to give the error estimates in order to obtain asymptotic expansions with respect to $ε$ in the sense of arbitrarily higher order differentiability norms (Theorem 6.1, 6.2), when the supports of $f$ and $g_j$'s are contained in fixed compact sets. |
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書誌情報 |
Journal of mathematical sciences, the University of Tokyo 巻 3, 号 1, p. 199-246, 発行日 1996 |
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ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 13405705 | |||||
書誌レコードID | ||||||
収録物識別子タイプ | NCID | |||||
収録物識別子 | AA11021653 | |||||
フォーマット | ||||||
内容記述タイプ | Other | |||||
内容記述 | application/pdf | |||||
日本十進分類法 | ||||||
主題 | 415 | |||||
主題Scheme | NDC | |||||
Mathematical Reviews Number | ||||||
MR1414625 | ||||||
Mathmatical Subject Classification | ||||||
35L30(MSC1991) | ||||||
Mathmatical Subject Classification | ||||||
35B25(MSC1991) | ||||||
Mathmatical Subject Classification | ||||||
35C20(MSC1991) | ||||||
Mathmatical Subject Classification | ||||||
81Q20(MSC1991) | ||||||
出版者 | ||||||
出版者 | Graduate School of Mathematical Sciences, The University of Tokyo | |||||
原稿受領日 | ||||||
1994-04-11 |