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 Izv. RAN. Ser. Mat., 2001, Volume 65, Issue 4, Pages 67–88 (Mi izv348)

A priori estimates for the solution of the first boundary-value problem for a class of second-order parabolic systems

L. I. Kamynin, B. N. Khimchenko

Abstract: We consider two classes of second-order parabolic matrix-vector systems (with solutions $u\in M_{m\times 1}$, $m\geqslant 2$) that can be reduced to a single second-order parabolic equation for a scalar function $v=\langle p,u\rangle$, where $p\in M_{m\times 1}$ is a fixed stochastic constant vector. We consider the first boundary-value problem for a scalar second-order parabolic equation (with unbounded coefficients) in a domain unbounded with respect to $x$ under the assumption of strong absorption at infinity. We obtain an a priori estimate for solutions of the first boundary-value problem in the generalized Tikhonov–Täcklind classes. (The problem under investigation has at most one solution in these classes.)

DOI: https://doi.org/10.4213/im348

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English version:
Izvestiya: Mathematics, 2001, 65:4, 705–726

Bibliographic databases:

MSC: 35K50, 35B50, 35K20, 35B45, 35K15, 35A05, 35B05

Citation: L. I. Kamynin, B. N. Khimchenko, “A priori estimates for the solution of the first boundary-value problem for a class of second-order parabolic systems”, Izv. RAN. Ser. Mat., 65:4 (2001), 67–88; Izv. Math., 65:4 (2001), 705–726

Citation in format AMSBIB
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\by L.~I.~Kamynin, B.~N.~Khimchenko
\paper A~priori estimates for the solution of the first boundary-value problem for a~class of second-order parabolic systems
\jour Izv. RAN. Ser. Mat.
\yr 2001
\vol 65
\issue 4
\pages 67--88
\mathnet{http://mi.mathnet.ru/izv348}
\crossref{https://doi.org/10.4213/im348}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1857711}
\zmath{https://zbmath.org/?q=an:1028.35028}
\transl
\jour Izv. Math.
\yr 2001
\vol 65
\issue 4
\pages 705--726
\crossref{https://doi.org/10.1070/IM2001v065n04ABEH000348}
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