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Mat. Sb. (N.S.), 1984, Volume 125(167), Number 1(9), Pages 19–37 (Mi msb2070)  

This article is cited in 12 scientific papers (total in 12 papers)

Nonhomogeneous boundary value problems for differential-operator equations of mixed type, and their application

N. V. Kislov

Abstract: Let $A$ and $B$ be symmetric operators in a Hilbert space $H$, such that $B$ is positive and $A$ has an arbitrary spectrum. In this paper nonhomogeneous boundary value problems are considered for an equation of the form
\begin{equation} Au'(t)+Bu(t)=f(t),\qquad t\in(0,T). \end{equation}

An abstract theorem (of the Lax–Milgram type) is proved, which is then used to prove theorems on the weak and strong solvability of boundary value problems for equation (1) in the energy spaces defined by the operators $A$ and $B$, as well as a theorem on the traces of a strong solution.
As an application, nonhomogeneous boundary value problems for partial differential equations are considered.
Bibliography: 16 titles.

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English version:
Mathematics of the USSR-Sbornik, 1986, 53:1, 17–35

Bibliographic databases:

UDC: 517.95
MSC: Primary 35M05, 47A50, 47F05; Secondary 35R20
Received: 10.06.1983

Citation: N. V. Kislov, “Nonhomogeneous boundary value problems for differential-operator equations of mixed type, and their application”, Mat. Sb. (N.S.), 125(167):1(9) (1984), 19–37; Math. USSR-Sb., 53:1 (1986), 17–35

Citation in format AMSBIB
\by N.~V.~Kislov
\paper Nonhomogeneous boundary value problems for differential-operator equations of mixed type, and their application
\jour Mat. Sb. (N.S.)
\yr 1984
\vol 125(167)
\issue 1(9)
\pages 19--37
\jour Math. USSR-Sb.
\yr 1986
\vol 53
\issue 1
\pages 17--35

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    This publication is cited in the following articles:
    1. Egorov I., “Boundary-Problem for One High-Order Equation with Changing Time Direction”, 303, no. 6, 1988, 1301–1304  mathscinet  isi
    2. S. G. Pyatkov, “Riesz completeness of the eigenelements and associated elements of linear selfadjoint pencils”, Russian Acad. Sci. Sb. Math., 81:2 (1995), 343–361  mathnet  crossref  mathscinet  zmath  isi
    3. Lomovtsev F., “Abstract Evolution Differential Equations with Discontinuous Operator Coefficients”, Differ. Equ., 31:7 (1995), 1067–1076  mathnet  mathscinet  zmath  isi
    4. S. G. Pyatkov, “Boundary Value Problems for Some Classes of Singular Parabolic Equations”, Siberian Adv. Math., 14:3 (2004), 63–125  mathnet  mathscinet  zmath  elib
    5. S. N. Glazatov, “Some nonclassical boundary value problems for linear mixed-type equations”, Siberian Math. J., 44:1 (2003), 37–43  mathnet  crossref  mathscinet  zmath  isi
    6. S. A. Zagrebina, “O zadache Dirikhle–Verigina dlya lineinogo uravneniya Oskolkova”, Vestnik ChelGU, 2003, no. 7, 57–65  mathnet
    7. Sergey Pyatkov, Sergey Popov, Vasilii Antipin, “On Solvability of Boundary Value Problems for Kinetic Operator-Differential Equations”, Integr. Equ. Oper. Theory, 2014  crossref
    8. K. S. Fayazov, I. O. Khazhiev, “Conditional correctness of boundary-value problem for composite fourth-order differential equation”, Russian Math. (Iz. VUZ), 59:4 (2015), 54–62  mathnet  crossref
    9. I. M. Petrushko, M. I. Petrushko, “O pervoi smeshannoi zadache dlya vyrozhdayuschikhsya parabolicheskikh uravnenii s menyayuschimsya napravleniem vremeni”, Matematicheskie zametki SVFU, 23:1 (2016), 67–78  mathnet  elib
    10. E. S. Efimova, “Statsionarnyi metod Galerkina dlya polulineinogo neklassicheskogo uravneniya vysokogo poryadka s menyayuschimsya napravleniem vremeni”, Matematicheskie zametki SVFU, 24:1 (2017), 16–25  mathnet  elib
    11. A. I. Kozhanov, S. V. Potapova, “Boundary value problems for odd order forward-backward-type differential equations with two time variables”, Siberian Math. J., 59:5 (2018), 870–884  mathnet  crossref  crossref  isi  elib
    12. S. G. Pyatkov, “On Some Classes of Nonlocal Boundary-Value Problems for Singular Parabolic Equations”, Math. Notes, 106:4 (2019), 602–615  mathnet  crossref  crossref  isi  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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