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 Mat. Sb. (N.S.), 1981, Volume 114(156), Number 4, Pages 523–565 (Mi msb2350)

Green's matrices of boundary value problems for Petrovskii parabolic systems of general form. II

S. D. Ivasishen

Abstract: Green's matrices are constructed for general nonhomogeneous boundary value problems for Petrovskii parabolic systems of differential equations of arbitrary order in unbounded as well as bounded domains with smooth, generally noncylindrical, lateral boundaries. The properties of these matrices are studied, and sharp estimates obtained for their derivatives with respect to all arguments.
For Part I, see Mat. Sb. (N.S.), v. 114(156) (1981), 110–166.
Bibliography: 5 titles.

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English version:
Mathematics of the USSR-Sbornik, 1982, 42:4, 461–498

Bibliographic databases:

UDC: 517.946
MSC: Primary 35K50; Secondary 35B45

Citation: S. D. Ivasishen, “Green's matrices of boundary value problems for Petrovskii parabolic systems of general form. II”, Mat. Sb. (N.S.), 114(156):4 (1981), 523–565; Math. USSR-Sb., 42:4 (1982), 461–498

Citation in format AMSBIB
\Bibitem{Iva81} \by S.~D.~Ivasishen \paper Green's matrices of boundary value problems for Petrovskii parabolic systems of general form.~II \jour Mat. Sb. (N.S.) \yr 1981 \vol 114(156) \issue 4 \pages 523--565 \mathnet{http://mi.mathnet.ru/msb2350} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=615340} \zmath{https://zbmath.org/?q=an:0484.35048|0468.35049} \transl \jour Math. USSR-Sb. \yr 1982 \vol 42 \issue 4 \pages 461--498 \crossref{https://doi.org/10.1070/SM1982v042n04ABEH002386} 

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This publication is cited in the following articles:
1. Drin M., Ivasishen S., “Greens Matrix of a General Boundary-Value Problem for the Petrovsky,I.G. Parabolic-System with Discontinuous Coefficients”, no. 11, 1984, 7–10
2. Ivasishen S., “Conjugate Greens Operators and the Correct Solvability of Parabolic Boundary-Value Problem in Negative Holder Spaces”, Differ. Equ., 20:3 (1984), 363–372
3. V. A. Kozlov, “The Green function and Poisson kernels of a parabolic problem in a domain with a conical point”, Russian Math. Surveys, 43:3 (1988), 211–213
4. Akhmetov, DR, “A criterion for existence of L-1-norms for higher-order derivatives of solutions to a homogeneous parabolic equation”, Siberian Mathematical Journal, 41:3 (2000), 405
5. Menaldi J.-L., Tubaro L., “Green and Poisson Functions with Wentzell Boundary Conditions”, J. Differ. Equ., 237:1 (2007), 77–115
6. Gurevich P., Tikhomirov S., “Uniqueness of Transverse Solutions for Reaction-Diffusion Equations with Spatially Distributed Hysteresis”, Nonlinear Anal.-Theory Methods Appl., 75:18 (2012), 6610–6619
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