RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Sb.: Year: Volume: Issue: Page: Find

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

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
$$Au'(t)+Bu(t)=f(t),\qquad t\in(0,T).$$

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.

Full text: PDF file (977 kB)
References: PDF file   HTML file

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

Bibliographic databases:

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

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
\Bibitem{Kis84} \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 \mathnet{http://mi.mathnet.ru/msb2070} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=760412} \zmath{https://zbmath.org/?q=an:0607.47045} \transl \jour Math. USSR-Sb. \yr 1986 \vol 53 \issue 1 \pages 17--35 \crossref{https://doi.org/10.1070/SM1986v053n01ABEH002908} 

• http://mi.mathnet.ru/eng/msb2070
• http://mi.mathnet.ru/eng/msb/v167/i1/p19

 SHARE:

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. Egorov I., “Boundary-Problem for One High-Order Equation with Changing Time Direction”, 303, no. 6, 1988, 1301–1304
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
3. Lomovtsev F., “Abstract Evolution Differential Equations with Discontinuous Operator Coefficients”, Differ. Equ., 31:7 (1995), 1067–1076
4. S. G. Pyatkov, “Boundary Value Problems for Some Classes of Singular Parabolic Equations”, Siberian Adv. Math., 14:3 (2004), 63–125
5. S. N. Glazatov, “Some nonclassical boundary value problems for linear mixed-type equations”, Siberian Math. J., 44:1 (2003), 37–43
6. S. A. Zagrebina, “O zadache Dirikhle–Verigina dlya lineinogo uravneniya Oskolkova”, Vestnik ChelGU, 2003, no. 7, 57–65
7. Sergey Pyatkov, Sergey Popov, Vasilii Antipin, “On Solvability of Boundary Value Problems for Kinetic Operator-Differential Equations”, Integr. Equ. Oper. Theory, 2014
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
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
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
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
12. S. G. Pyatkov, “On Some Classes of Nonlocal Boundary-Value Problems for Singular Parabolic Equations”, Math. Notes, 106:4 (2019), 602–615
•  Number of views: This page: 422 Full text: 146 References: 37 First page: 1