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Cauchy problem for parabolic equations of Shilov type with variable coefficients
Dovzhytska Iryna Mykhailivna 1 , Litovchenko Vladyslav Antonovich 1
1 Department of Differential Equations, Yuriy Fedkovych Chernivtsi National University, Chernivtsi, 58000, Ukraine
Keywords: Cauchy problem, parabolic equations of Shilov type
Abstract
We established the correct solvability of Cauchy problem for a class of Shhov type parabolic equations with smooth bounded variable coeffidents and nonnegative genus іп the case of initial data belonging to wide class of general functions.
References

[1] Zhitomirskiy, Ya.I. Cauchy problem for some types of parabolic by G.E. Shilov systems of linear equations in partial derivatives with continuous coefficients // Izv. of the USSR Academy of Sciences. Ser. matem. - 1959. - Т. 23. - P. 925-932.

[2] Dovzhytska I.M., Litovchenko V.A. Fundamental solution of the Cauchy problem for one class of parabolic equations with variable coefficients // Scientific Bulletin of Chernivtsi University. - 2010. - Issue 528. - P. 43-50.

[3] Gelfand I.M., Shilov G.E. Some questions of the theory of differential equations.  - M.: Fizmatgiz, 1958. - 274 p.

[4] Gelfand I.M., Shilov G.E. Spaces of basic and generalized functions.  - M.: Fizmatgiz, 1958. - 307 p.

[5] Litovchenko V.A. Cauchy problem for parabolic Shilov equations // Siberian Mathematical Journal - 2004. - Vol. 45, № 4. - P. 809-821.

Cite
ACS Style
Dovzhytska, I.M.; Litovchenko, V.A. Cauchy problem for parabolic equations of Shilov type with variable coefficients. Bukovinian Mathematical Journal. 2018, 2
AMA Style
Dovzhytska IM, Litovchenko VA. Cauchy problem for parabolic equations of Shilov type with variable coefficients. Bukovinian Mathematical Journal. 2018; 2(1).
Chicago/Turabian Style
Iryna Mykhailivna Dovzhytska, Vladyslav Antonovich Litovchenko. 2018. "Cauchy problem for parabolic equations of Shilov type with variable coefficients". Bukovinian Mathematical Journal. 2 no. 1.
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