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 Mat. Sb. (N.S.), 1987, Volume 133(175), Number 4(8), Pages 539–555 (Mi msb2630)

On boundary value problems for a class of ultraparabolic equations, and their applications

S. A. Tersenov

Abstract: Let $\lambda_i(t)\ge\alpha>0$, and let $L$ be a strictly elliptic operator of second order in space variables $x$, with coefficients depending only on $x=(x_1,…,x_m)$.
Using potentials, solutions of some initial-boundary value problems for the ultraparabolic equation $\sum^n_{i=1}\lambda_i(x)\frac{\partial u}{\partial t_i}=L(u)$ are constructed. These solutions belong to special Hölder spaces $H^{P,P/2}_{x\lambda}$ depending on the vector $\lambda=(\lambda_1,…,\lambda_n)$. By means of these notions the first boundary value problem for the equation $\sum^n_{i=1}\lambda_i\frac{\partial u}{\partial t_i}=u_{xx}\operatorname{sgn}x$ is studied in a domain containing the hyperplane $x=0$. Necessary and sufficient conditions for the existence of a solution of this problem in the spaces $H^{P,P/2}_{x\lambda}$ are given.
Bibliography: 14 titles.

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English version:
Mathematics of the USSR-Sbornik, 1988, 61:2, 529–544

Bibliographic databases:

UDC: 517.946
MSC: 35K70, 35K20

Citation: S. A. Tersenov, “On boundary value problems for a class of ultraparabolic equations, and their applications”, Mat. Sb. (N.S.), 133(175):4(8) (1987), 539–555; Math. USSR-Sb., 61:2 (1988), 529–544

Citation in format AMSBIB
\Bibitem{Ter87} \by S.~A.~Tersenov \paper On boundary value problems for a~class of ultraparabolic equations, and their applications \jour Mat. Sb. (N.S.) \yr 1987 \vol 133(175) \issue 4(8) \pages 539--555 \mathnet{http://mi.mathnet.ru/msb2630} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=911807} \zmath{https://zbmath.org/?q=an:0699.35159|0669.35058} \transl \jour Math. USSR-Sb. \yr 1988 \vol 61 \issue 2 \pages 529--544 \crossref{https://doi.org/10.1070/SM1988v061n02ABEH003222} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. Tersenov A., “A-Priori Estimations of Solutions for One Class of Degenerating Parabolic and Ultraparabolic Equations”, Dokl. Akad. Nauk, 338:2 (1994), 168–170
2. Tersenov S., “On the First Boundary Problem for Parabolic Equation with Varying Sense of Time”, Dokl. Akad. Nauk, 348:1 (1996), 27–29
3. Lorenzi A., “Identification Problems in Banach Spaces for Linear First-Order Partial Differential Equations in One Space Dimension and Applications”, J. Inverse Ill-Posed Probl., 20:1 (2012), 65–102
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