Cauchy problem for degenerate parabolic systems of Kolmogorov-type equations with constant coefficients

Litovchenko Vladyslav Antonovich; Vasko Olena Borysivna

Litovchenko Vladyslav Antonovich ¹ , Vasko Olena Borysivna ¹

¹ Department of Differential Equations, Yuriy Fedkovych Chernivtsi National University, Chernivtsi, 58000, Ukraine

Keywords: degenerate parabolic systems of Kolmogorov-type equations, Cauchy problem

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Abstract

We establish the well solvability of the Cauchy problem with generalized initial data for a class of degenerate parabolic systems of Kolmogorov type equations with constant coefficients in the class of infinitely differentiable functions.

References

[1] Kolmogoroff A.N. Zufällige Bewegungen (Zur Theorie der Brownishen Bewegungen)// Ann. Math. – 1934. – 35 – P.116-117.

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

[3] Malitskaya G.P. Systems of equations of Kolmogorov type // Ukrainian Mathematical Journal - 2008. - 60, N12. - P.1650-1663.

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

[5] Ivasyshen S.D., Litovchenko V.A. Koshy problem for one class of degenerate parabolic equations of Kolmogorov type with positive genus // Ukrainian Mathematical Journal - 2009. - 61, N8. - P.1066-1087.

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ACS Style: Litovchenko, V.A.; Vasko, O.B. Cauchy problem for degenerate parabolic systems of Kolmogorov-type equations with constant coefficients. Bukovinian Mathematical Journal. 2016, 1
AMA Style: Litovchenko VA, Vasko OB. Cauchy problem for degenerate parabolic systems of Kolmogorov-type equations with constant coefficients. Bukovinian Mathematical Journal. 2016; 1(1-2).
Chicago/Turabian Style: Vladyslav Antonovich Litovchenko, Olena Borysivna Vasko. 2016. "Cauchy problem for degenerate parabolic systems of Kolmogorov-type equations with constant coefficients". Bukovinian Mathematical Journal. 1 no. 1-2.

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