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Mat. Sb., 2003, Volume 194, Number 5, Pages 3–30 (Mi msb733)  

This article is cited in 4 scientific papers (total in 4 papers)

The defining boundary conditions and the degenerate problem for elliptic boundary-value problems with a small parameter in the highest derivatives

S. A. Golopuz

Vladimir State University

Abstract: For an elliptic equation with a small parameter multiplying the highest derivatives one considers a boundary-value problem such that some of the orders of the last $p$ boundary conditions are congruent modulo $2p$ (here $2p$ is the difference between the orders of the perturbed and the non-perturbed equations). In the case when no three of them are congruent modulo $2p$, associated boundary conditions are obtained and results on the asymptotic expansion are established.

DOI: https://doi.org/10.4213/sm733

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English version:
Sbornik: Mathematics, 2003, 194:5, 641–668

Bibliographic databases:

UDC: 517.956
MSC: Primary 35B25; Secondary 35J55
Received: 04.06.2002

Citation: S. A. Golopuz, “The defining boundary conditions and the degenerate problem for elliptic boundary-value problems with a small parameter in the highest derivatives”, Mat. Sb., 194:5 (2003), 3–30; Sb. Math., 194:5 (2003), 641–668

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. A. Golopuz, “Asymptotic Expansion of Solutions to Elliptic Boundary Value Problems in Certain Critical Cases”, Proc. Steklov Inst. Math., 250 (2005), 47–55  mathnet  mathscinet  zmath
    2. L. V. Korobenko, V. Zh. Sakbaev, “Formulation and well-posedness of the Cauchy problem for a diffusion equation with discontinuous degenerating coefficients”, Comput. Math. Math. Phys., 49:6 (2009), 1037–1053  mathnet  crossref  zmath  isi  elib
    3. S. A. Golopuz, “Adjoint boundary conditions for incomplete systems of initial relations between coefficients of the boundary layer”, Journal of Mathematical Sciences, 199:5 (2014), 535–546  mathnet  crossref  mathscinet
    4. V. Zh. Sakbaev, “Cauchy problem for degenerating linear differential equations and averaging of approximating regularizations”, Journal of Mathematical Sciences, 213:3 (2016), 287–459  mathnet  crossref  mathscinet
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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