Integral representation of solutions of some parabolic equations with the Bessel operator and increasing coefficients

Balabushenko Tonya Mykhailivna; Ivasyshen Stepan Dmytrovych; Lavrenchuk Volodymyr Petrovych; Melnychuk Liliia Mykhailivna

Balabushenko Tonya Mykhailivna ¹ , Ivasyshen Stepan Dmytrovych ² , Lavrenchuk Volodymyr Petrovych ³ , Melnychuk Liliia Mykhailivna ⁴

¹ Department of Mathematical Modeling, Yuriy Fedkovych Chernivtsi National University, Chernivtsi, 58000, Ukraine

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

³ Department of Higher Mathematics and Engineering and Technical Disciplines, Chernivtsi Institute of Trade and Economics of the Kyiv National University of Trade and Economics, Chernivtsi, 58002, Ukraine

⁴ Department of Differential Equations, Yuriy Fedkovych Chernivtsi National University, Chernivtsi, 58000, Ukraine

Keywords: integral representation, parabolic equations, Bessel operator

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Abstract

For a class of parabolic equations with growing coefficients on a variable $x ∈ \mathbb{R}^n$ an $|x| → ∞$ and with Bessel operator with respect to variable $y ∈ \mathbb{R}$ theorems of representation as Poisson integrals of solutions of the Cauchy problem and of solutions, determined in an open half-sphere, from special weight $L_p$-spaces are proved.

References

[1] Balabushenko T.M., Ivasyshen S.D., Lavrenchuk V.P., Melnychuk L.M. Fundamental solution of the Cauchy problem for some parabolic equations with the Bessel operator and increasing coefficients // Nauk. Bulletin of Chernivtsi University: 3b. scientific pr. Issue 288. Mathematics. - Chernivtsi: Ruta, 2005. - P.5 - 11.

[2] Balabushenko T.M., Ivasyshen S.D., Lavrenchuk V.P., Melnychuk L.M. Cauchy problem for some parabolic equations with the Bessel operator and increasing coefficients // Nauk. Bulletin of Chernivtsi University: Collected scientific pr. Issues 314 - 315. Mathematics. - Chernivtsi: Ruta, 2006. - P.7 - 16.

[3] Ivasishen S.D., Lavrenchuk V.P. On the integral representation of solutions of a parabolic system of linear equations with the Bessel operator // Nonlinear boundary problems. - 1992. - Issue. 4. - P. 19-25.

[4] Ivasishin L.M. Integral representation and sets of initial values of solutions of parabolic equations with Bessel operator and increasing coefficients. - Chernivtsi, 1992. 62 p. Dep. in UkrINTEI 26.10.92, № 1731 - Uk92.

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ACS Style: Balabushenko, T.M.; Ivasyshen, S.D.; Lavrenchuk, V.P.; Melnychuk, L.M. Integral representation of solutions of some parabolic equations with the Bessel operator and increasing coefficients. Bukovinian Mathematical Journal. 2018, 1
AMA Style: Balabushenko TM, Ivasyshen SD, Lavrenchuk VP, Melnychuk LM. Integral representation of solutions of some parabolic equations with the Bessel operator and increasing coefficients. Bukovinian Mathematical Journal. 2018; 1(336).
Chicago/Turabian Style: Tonya Mykhailivna Balabushenko, Stepan Dmytrovych Ivasyshen, Volodymyr Petrovych Lavrenchuk, Liliia Mykhailivna Melnychuk. 2018. "Integral representation of solutions of some parabolic equations with the Bessel operator and increasing coefficients". Bukovinian Mathematical Journal. 1 no. 336.

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