On the characterization of solutions of a single parabolic equation with increasing coefficients in the group of lower terms

Ivasyshen Stepan Dmytrovych; Pasichnyk Halyna

Ivasyshen Stepan Dmytrovych ¹ , Pasichnyk Halyna ²

¹ Department of Mathematical Physics and Differential Equations, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, 01001, Ukraine

² Department of Mathematical Modeling, Yuriy Fedkovych Chernivtsi National University, Chernivtsi, 58000, Ukraine

Keywords: parabolic equation with increasing coefficients, parabolic equation of Kolmogorov type, the Cauchy problem

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Abstract

The approach initiated by S.D. Eidelman that allows to get accurate results about the correct solvability of the Cauchy problem and the integral representation of the solutions that enables to characterize the relevant classes of solutions completely is realized for the second order degenerate parabolic equation of Kolmogorov type with the constant coefficients in a group of its highest terms and with the growing coefficients in a group of its lowest terms.

References

[1] Eidelman, S.D. Fundamental matrices of solutions of general parabolic systems / S.D. Eidelman // Dokl. of the USSR Academy of Sciences. - 1958. - 120, №5. - P. 980-983.

[2] Eidelman, S.D. Parabolic systems / S.D. Eidelman. - M.: Nauka, 1964. - 443 p.

[3] Eidelman S.D. Analytic methods in the theory of differential and pseudo-differential equations of parabolic type / S.D. Eidelman , S.D. Ivasyshen, A.N. Kochubei // Operator Theory: Adv. and Appl. - 2004. - 152 . - 390 p.

[4] Ivasyshen S.D. Solutions of parabolic equations from families of Banach spaces depending on time / Ivasyshen S.D. // Mat. - 2013. - 40 , № 2. - P. 172-181.

[5] Ivasyshen S.D. Fundamental solution of the Cauchy problem for one parabolic equation with increasing coefficients of the group of younger members / Ivasyshen S.D., Pasichnyk G.S. // Proceedings of the Institute of Mathematics of the National Academy of Sciences of Ukraine. - 2014. - 11 , №2. - P. 126-153.

[6] Ivasyshen S. Cauchy problem for one parabolic equation with increasing coefficients in the group of younger members / Stepan Ivasyshen, Halyna Pasichnyk // Mat. T. Shevchenko. - 2014. - 11 . - P. 73-87.

[7] Ivasyshen S.D. Integral image of solutions of one parabolic equation with increasing coefficients in the group of younger members / Ivasyshen S.D., Pasichnyk H.S. // Proceedings of the Institute of Mathematics of the National Academy of Sciences of Ukraine. - 2015. - 12 , № 2. - P. 205-229.

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Cite

ACS Style: Ivasyshen, S.D.; Pasichnyk, H. On the characterization of solutions of a single parabolic equation with increasing coefficients in the group of lower terms. Bukovinian Mathematical Journal. 2016, 3
AMA Style: Ivasyshen SD, Pasichnyk H. On the characterization of solutions of a single parabolic equation with increasing coefficients in the group of lower terms. Bukovinian Mathematical Journal. 2016; 3(3-4).
Chicago/Turabian Style: Stepan Dmytrovych Ivasyshen, Halyna Pasichnyk. 2016. "On the characterization of solutions of a single parabolic equation with increasing coefficients in the group of lower terms". Bukovinian Mathematical Journal. 3 no. 3-4.

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