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Mathematics of the USSR-Sbornik, 1971, Volume 13, Issue 1, Pages 25–64
DOI: https://doi.org/10.1070/SM1971v013n01ABEH001028
(Mi sm3028)
 

This article is cited in 19 scientific papers (total in 20 papers)

Boundary value problems for systems with a parameter

M. S. Agranovich
References:
Abstract: The paper is concerned with problems of the form
$$ A\biggl (x,\frac\partial{\partial x},p\biggr)u(x)=f(x)\quad\text{in}\quad G,\qquad B\biggl(x,\frac\partial{\partial x},p\biggr)u(x)=g(x)\quad\text{on}\quad\Gamma. $$
Here $G$ is a region in $R_x^n$ with smooth boundary $\Gamma$; $A$ and $B$ are matrices of linear partial differential operators with smooth coefficients, depending polynomially on the complex parameter $p$. The operator $A$ is obtained by replacing $\partial/\partial x$ by $p$ in the operator $A(x,\partial/\partial x,\partial/\partial t)$, which is strongly hyperbolic in the sense of I. G. Petrovskii. Under some supplementary assumptions, the existence and uniqueness of a strong solution in the spaces $H_{qs}$ is demonstrated, and an a priori estimate in norms involving the parameter $p$ is obtained for large values $\operatorname{Re}p$.
Bibliography: 30 titles.
Received: 29.05.1970
Bibliographic databases:
UDC: 517.944.4
Language: English
Original paper language: Russian
Citation: M. S. Agranovich, “Boundary value problems for systems with a parameter”, Math. USSR-Sb., 13:1 (1971), 25–64
Citation in format AMSBIB
\Bibitem{Agr71}
\by M.~S.~Agranovich
\paper Boundary value problems for systems with a~parameter
\jour Math. USSR-Sb.
\yr 1971
\vol 13
\issue 1
\pages 25--64
\mathnet{http://mi.mathnet.ru//eng/sm3028}
\crossref{https://doi.org/10.1070/SM1971v013n01ABEH001028}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=285808}
\zmath{https://zbmath.org/?q=an:0207.10801|0238.35014}
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  • https://doi.org/10.1070/SM1971v013n01ABEH001028
  • https://www.mathnet.ru/eng/sm/v126/i1/p27
  • This publication is cited in the following 20 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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