Correct solvability of the model $\overrightarrow{2b}$-parabolic boundary value problem in Hölder spaces

Turchyna  Natalia Ivanivna; Ivasyshen Stepan Dmytrovych

doi:https://doi.org/10.31861/bmj2018.03.152

Turchyna Natalia Ivanivna ¹ , Ivasyshen Stepan Dmytrovych ²

¹ National Technical University of Ukraine "Kyiv Polytechnic Institute named after Igor Sikorsky ", Kyiv, 03056, Ukraine

² Department of Mathematical Physics and Differential Equations, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, 01001, Ukraine

DOI: https://doi.org/10.31861/bmj2018.03.152

Keywords: 2b-parabolic boundary value problem, correct solvability, correct solvability of sucha problem in the H ̈older space, exact estimates

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Abstract

The general model $\overrightarrow{2b}$ -parabolic boundary value problem is considered. The theorem on the correct solvability of such a problem in the Höelder spaces is proved. Exact estimates of the norms of the solution through the corresponding norms of the right parts of the problem are obtained. It is established that for the correctness of such estimates the conditions of $\overrightarrow{2b}$ -parabolicity of the problem are not only sufficient but also necessary.

References

[1] Turchyna N. I., Ivasyshen S. D. About the model of the boundary value problem in the vector vector // Bukovinsky mat. journ - 2017 - 5, N 3-4. - P. 163-167.

[2] Turchyna N. I., Ivasyshen S. D. Grin Matrix of a Model Boundary Value Problem with Vector Parabolic Weight // Mat. methods and phys.-fur. fields - 2017 - 60, N 4. - S. 25-39.

[3] Ladyzhenskaia O. A., Solonnykov V. A., Uraltseva N. N. Linear and quasilinear equations of a parabolic type. - Moscow: Science, 1967. - 736 p.

[4] Yvasyshen S. D. Linear parabolic boundary value problems. - Kiev: Higher school, 1987. - 72 p. - (Modern achievements of mathematics and its applications).

[5] Yvasyshen S. D., Eidelman S. D. $overrightarrow{2b}$ parabolic systems // Tr. workshop on functional analysis - Kyiv: Institute of Mathematics, Academy of Sciences of the Ukrainian SSR, 1968. - Izp. 1. - P. 3-175, 271-273.

[6] Eidelman S. D., Ivasyshen S. D., Kochubei AN. Analytic methods in the theory of differential equations and pseudo-di ff erential equations of parabolic type // Operator Theory: Advances and Applications. - 2004 -152 -390 p.

https://doi.org/10.1007/978-3-0348-7844-9

[7] Ivasyshen S. D., Ivasiuk H. P. Correct solvability of Solan'nikov-Eidlmann's parabolic initial problems // Ukr. mate. journ - 2009. - 61, N 5. - C. 650-671.

https://doi.org/10.1007/s11253-009-0244-7

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Cite

ACS Style: Turchyna , N.I.; Ivasyshen, S.D. Correct solvability of the model $\overrightarrow{2b}$-parabolic boundary value problem in Hölder spaces. Bukovinian Mathematical Journal. 2019, 6 https://doi.org/https://doi.org/10.31861/bmj2018.03.152
AMA Style: Turchyna NI, Ivasyshen SD. Correct solvability of the model $\overrightarrow{2b}$-parabolic boundary value problem in Hölder spaces. Bukovinian Mathematical Journal. 2019; 6(3-4). https://doi.org/https://doi.org/10.31861/bmj2018.03.152
Chicago/Turabian Style: Natalia Ivanivna Turchyna , Stepan Dmytrovych Ivasyshen. 2019. "Correct solvability of the model $\overrightarrow{2b}$-parabolic boundary value problem in Hölder spaces". Bukovinian Mathematical Journal. 6 no. 3-4. https://doi.org/https://doi.org/10.31861/bmj2018.03.152

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