Abstract:
The boundary value problem for mixed type equation with nonlocal initial conditions in integral form is considered. The main result states that the nonlocal problem is equivalent to the classical boundary value problem for a loaded equation. This fact helps to prove the uniqueness and, under extra restrictions, the existence of a generalized solution of the problem.
Keywords:
mixed type equation, nonlocal conditions, generalized solution.
Original article submitted 24/VII/2013 revision submitted – 09/VIII/2013
Citation:
S. V. Kirichenko, “On a boundary value problem for mixed type equation with nonlocal initial conditions in the rectangle”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 3(32) (2013), 185–189
\Bibitem{Kir13}
\by S.~V.~Kirichenko
\paper On a boundary value problem for mixed type equation with nonlocal initial conditions in the rectangle
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2013
\vol 3(32)
\pages 185--189
\mathnet{http://mi.mathnet.ru/vsgtu1248}
\crossref{https://doi.org/10.14498/vsgtu1248}
\zmath{https://zbmath.org/?q=an:06968795}
Linking options:
https://www.mathnet.ru/eng/vsgtu1248
https://www.mathnet.ru/eng/vsgtu/v132/p185
This publication is cited in the following 4 articles:
Buhrii O., Buhrii N., “Nonlocal in Time Problem For Anisotropic Parabolic Equations With Variable Exponents of Nonlinearities”, J. Math. Anal. Appl., 473:2 (2019), 695–711
E. Azizbayov, Y. Mehraliyev, “Solvability of nonlocal inverse boundary-value problem for a second-order parabolic equation with integral conditions”, Electronic Journal of Differential Equations, 2017 (2017), 125, 1–14
Azizbayov E., Mehraliyev Ya., “Solvability of Nonlocal Inverse Boundary-Value Problem For a Second-Order Parabolic Equation With Integral Conditions”, Electron. J. Differ. Equ., 2017, 125
Ya. T. Megraliev, F. Kh. Alizade, “Obratnaya kraevaya zadacha dlya odnogo uravneniya Bussineska chetvertogo poryadka s nelokalnymi integralnymi po vremeni usloviyami vtorogo roda”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 26:4 (2016), 503–514
Citation in format AMSBIB
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