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Fundamental solution of the Cauchy problem for one class of parabolic equations 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: fundamental solution, the Cauchy problem, parabolic equations with variable coefficients
Abstract

We constructed the fundamental solution of Cauchy problem and investigated it basic properties for a class of Shilov type parabolic equations with smooth variable coefficients.

References

[1] Zhytomyrskyi Y.I. Cauchy's problem for some types of parabolic according to G.E. Shilovu systems of linear equations in partial derivatives with continuous coefficients // Izv. Academy of Sciences of the USSR. Ser. we have - 1959. - 23. - P. 925 - 932.

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

[3] Lytovchenko V.A. Cauchy's problem for Shilov parabolic equations // Sib. mate. journal 2004. - T. 45, NÂș4. - P. 809-821.

[4] Friedman A. Equations with partial derivatives of the parabolic type. - M.: Mir, - 1968. 427 p.

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

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Cite
ACS Style
Dovzhytska, I.M.; Litovchenko, V.A. Fundamental solution of the Cauchy problem for one class of parabolic equations with variable coefficients. Bukovinian Mathematical Journal. 2018, 1
AMA Style
Dovzhytska IM, Litovchenko VA. Fundamental solution of the Cauchy problem for one class of parabolic equations with variable coefficients. Bukovinian Mathematical Journal. 2018; 1(528 ).
Chicago/Turabian Style
Iryna Mykhailivna Dovzhytska, Vladyslav Antonovich Litovchenko. 2018. "Fundamental solution of the Cauchy problem for one class of parabolic equations with variable coefficients". Bukovinian Mathematical Journal. 1 no. 528 .
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