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

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

S. A. Golopuz

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

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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• http://mi.mathnet.ru/eng/msb733
• https://doi.org/10.4213/sm733
• http://mi.mathnet.ru/eng/msb/v194/i5/p3

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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
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
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
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
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