Аннотация:
Elliptic partial differential equations have applications in almost all areas of mathematics, from harmonic analysis to geometry to Lie theory, as well as numerous applications in physics and engineering. The well-posedness of the local and nonlocal boundary-value problems for the elliptic equation in a Banach space with the positive operator and its
related applications have been investigated by many researchers (see, e.g., [1–4] and the references given therein). Recently, various nonlocal boundary-value problems with Samatskii–Ionkin condition for partial differential equations have been investigated by many
researchers (see, e.g., [5, 6] and the references given therein).
In the present paper, the well-posedness of the nonlocal boundary-value problem with Samarskii–
Ionkin condition for elliptic equations in a Banach space with a strongly positive operator is established.
In practice, the coercive stability estimates for the solution of four types of nonlocal boundary-value problems with Samatskii–Ionkin condition for elliptic differential equations are proved.
Список литературы
Ashyralyev A., Sobolevskii P. E., New Difference Schemes for Partial Differential Equations, Birkhäuser, Basel–Boston–Berlin, 2004
Lunardi A., Analytic Semigroups and Optimal Regularity in Parabolic Problems, Birkhäuser, Basel–Boston–Berlin, 1995
Skubachevskii A. L., Elliptic Functional Differential Equations and Applications, Birkhäuser, Basel–Boston–Berlin, 1997
Krein S. G., Linear differential Equations in Banach Space, AMS, Providence, 1971
Sadybekov M. A., Dukenbayeva A. A., “Direct and inverse problems for the Poisson equation with equality of flows on a part of the boundary”, Complex Variables and Elliptic Equations, 64:5 (2019), 777–791
Sadybekov M. A., Dukenbayeva A. A., “On boundary value problems of the Samarskii–Ionkin type for the Laplace operator in a ball”, Complex Variables and Elliptic Equations, 67:2 (2022), 369–383
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