A multipoint problem for equations with partial derivatives in a two-dimensional domain

Volianska Iryna; Il’kiv Volodymyr

doi:https://doi.org/10.31861/bmj2018.03.028

Volianska Iryna ¹ , Il’kiv Volodymyr ¹

¹ Department of Higher Mathematics, Lviv polytechnic national university, Lviv, 79007, Ukraine

DOI: https://doi.org/10.31861/bmj2018.03.028

Keywords: multi-point problem, one spatial variable

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Abstract

The multi-point problem for linear partial differential equation in a plane domain is investigated. Correctness after Hadamard of this problem is shown, which distinguishes it from the conditionally correct problem with many spatial variables. The existence and uniqueness conditions of the solution of problem in the spaces of periodic functions with an exponential change of Fourier coefficients are established.

References

Vasylyshyn P.B. Ptashnyk B.Y. Multi-point problem for integral-differential equations with partial derivatives. Ukr mate. journ 1998, 50 (9), 1155-1168.

https://doi.org/10.1007/BF02525240

Volianska I.I. Ilkiv V.S. Conditions for solving a three-point problem for a differential equation with partial derivatives in a two-dimensional cylinder. Laboratory of the Institute of Mathematics, National Academy of Sciences of Ukraine, 2015, 12 (2), 74-100.

Dykopolov H.V. Shylov H.E. On correct boundary-value problems for partial differential equations in a half-space. Izv. Academy of Sciences of the USSR. Sir Mat. 1960, 24 (3), 369-380.

Kaleniuk P. I., Volianska I. I., Ilkiv V. S., Nytrebych Z. M. On the uniquely solvability of a three-point problem for the equation with partial derivatives in a two-dimensional region. Mate. methods and phys.-fur. Fields 2017, 60 (3), 46-59.

Kaleniuk P. I., Nytrebych Z. M. Generalized scheme of separation of variables. Differential character method. View of the National University of Lviv Polytechnic, Lviv, 2002.

Klius I.S., Ptashnyk B.Y. Multi-point problem for pseudodifferential equations. Ukr mate. journ 2003, 55 (1), 21-29.

Lankaster P. Theory of Matrices. Science, Moscow, 1973.

Palamodov V.P. On correct boundary value problems for partial differential equations in a half-space. Izv. Academy of Sciences of the USSR. Sir Mat. 1960, 24 (3), 381-386.

Pokornyi Yu.V. Second solutions of the nonlinear Valle-Poussin problem. Differents Equations 1970, 6 (9), 1599-1605.

Ptashnyk B.Y. Inaccurate boundary value problems for differential equations with partial derivatives. Scientific Opinion, Kyiv, 1984.

Ptashnyk B.Y., Syliuha L.P. Multi-point problem for non-type differential equations with constant coefficients. References of NAS of Ukraine 1996, (3), 10-14.

Ptashnyk B.Y., Symotiuk M.M. Multi-point problem for nonisotropic differential equations with partial derivatives with constant coefficients. Ukr mate. journ 2003, 55 (2), 241-254.

Ptashnyk B.Y., Tymkiv I.R. Multi-point problem for a parabolic equation with varying coefficients in a cylindrical region. Mate. methods and phys.-fur. Fields 2011, 54 (1), 15-26.

Ptashnyk B.Y., Shtabaliuk P.Y. A boundary value problem for hyperbolic equations in a class of functions almost periodic in spatial variables. Differents Equations 1986, 22 (4), 669-678.

Horn R., Johnson C. Math. Analysis, World, Moscow, 1989.

Kalenyuk P.I., Kohut I.V., Nytrebych Z.M. An investigation into a problem with homogeneous local two-point conditions for a homogeneous system of partial differential equations. Journal of Mathematics Sciences 2011, 174 (2), 121-135. Doi: 10.1007 / s10958-011-0285-y (translation of the Mathematical Methods in Physics-Mekhanichni Polya 2009, 52 (4), 7-17. (In Ukrainian ))

https://doi.org/10.1007/s10958-011-0285-y

Kalenyuk P.I., Nytrebych Z.M. It is an operational method for solving initial-value problems for partial differential equations induced by a generalized separation of variables. Journal of Mathematics Sciences 1999, 97 (1), 38793887. (translation of the Mathematical Methods in Physics-Mekhanichni Polya 1998, 41 (1), 136-145).

https://doi.org/10.1007/BF02364928

Malanchuk O.M., Nytrebych Z.M. Homogeneous two-point froblem for PDE of the second order in the time variable and the in fi nite order in spatial variables. Open Mathematics 2017, 15 (1), 101-110.

https://doi.org/10.1515/math-2017-0009

Nitrebich Z.M. A boudary-value problem in an unbounded strip. Journal of Mathematical Sciences 1996,79 (6), 1388-1392. doi: 10.1007 / BF02362789 (translation of Mathematical Methods in Physics-Mekhanichni Polya 1994, (37), 16-21.)

https://doi.org/10.1007/BF02362789

Nytrebych Z.M., Ilkiv V.S., Pukach P.Ya. Homogeneous problem with two-point conditions in time for some equations of mathematical physics. Azerb Journal of Mathematics 2017, 7 (2), 180-196.

Nytrebych Z.M., Malanchuk O.M., Ilkiv V.S., Pukach P.Ya. On the solvability of a two-point problem in PDE. Italian Journal of Pure and Applied Mathematics 2017, (38), 715-726.

Symotyuk M. M., Tymkiv I.R. Problem with two-point conditions for parabolic equation of second order on time. Carpathian Matchematical Publication 2014, 6 (2), 351-359.

https://doi.org/10.15330/cmp.6.2.351-359

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ACS Style: Volianska, I.; Il’kiv, V. A multipoint problem for equations with partial derivatives in a two-dimensional domain. Bukovinian Mathematical Journal. 2019, 6 https://doi.org/ https://doi.org/10.31861/bmj2018.03.028
AMA Style: Volianska I, Il’kiv V. A multipoint problem for equations with partial derivatives in a two-dimensional domain. Bukovinian Mathematical Journal. 2019; 6(3-4). https://doi.org/ https://doi.org/10.31861/bmj2018.03.028
Chicago/Turabian Style: Iryna Volianska, Volodymyr Il’kiv. 2019. "A multipoint problem for equations with partial derivatives in a two-dimensional domain". Bukovinian Mathematical Journal. 6 no. 3-4. https://doi.org/ https://doi.org/10.31861/bmj2018.03.028

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