Перейти до основного вмісту
Properties of integrals which have the type of derivatives of volume potentials for degenerated $\overrightarrow{2b}$ -parabolic equation of Kolmogorov type
Dron’ Vitaly 1 , Medynsky Igor 2
1 Laboratory of Mathematical Physics, Pidstryhach Institute for Applied Problems of Mechanics and Mathematics National Academy of Sciences of Ukraine, Lviv, 79007, Ukraine
2 Department of Applied Mathematics, Lviv polytechnic national university, Lviv, 79007, Ukraine
Keywords: $\overrightarrow{2b}$-parabolic equation of Kolmogorov type, an integral which have the type of derivatives of the volume potential,, weighted H ̈older norm, H ̈older space ofincreasing functions
Abstract
In weighted H ̈older spaces it is studied the smoothness of integrals, which have the structure and properties of derivatives of volume potentials which generated by fundamental solution of the Cauchy problem for degenerated $\overrightarrow{2b}$-parabolic equation of Kolmogorov type. The coefficients in this equation depend only on the time variable. Special distances and norms are used for constructing of the weighted H ̈older spaces.
The results of the paper can be used for establishing of the correct solvability of the Cauchy problem and estimates of solutions of the given non-homogeneous equation in corresponding weighted H ̈older spaces.
References

[1] Eidelman S.D. Parabolic Systems. North-Holland, Amsterdam, 1969 (Russian edition. Nauka, Moskow, 1964).
[2] Eidelman S.D., Ivasyshen S.D., Kochubei A.N. Analytic methods in the theory of differential and pseudo-differential equations of parabolic type. Birkhauser. Basel, 2004, Ser. Operator Theory: Adv. and Appl., Vol. 152. https://doi.org./10.1007/978-3-0348-7844-9.
[3] Dron’ V.S., Ivasyshen S.D., Medynsky I.P. Properties of integrals which have the type of derivatives of volume potentials for one Kolmogorov type ultraparabolic arbitrary order equation. Carpatian Math. Publ. 2019, 11 (2). 268–280. doi:10.15330/cmp.11.2.268-280
[4] Ivasyshen S.D., Medynsky I.P. Properties of integrals which have the type of derivatives of volume potentials for parabolic systems with degeneration on the initial hypeplane. Mat. Studii 2000, 13(1), 33–46.
[5] Dron’ V.S. On correct solvability in weighted Holder spaces for the Cauchy problem for a class of degenerate parabolic equations of the Kolmogorov type. Nauk. Visnyk Chernivtsi University 2000, No.76, 32–41 (in Ukrainian).
[6] Dron’ V.S., Ivasyshen S.D. On properties of the volume potential and correct solvability of the Cauchy problem for a model ultraparabolic equation. Nauk. Visnyk Chernivtsi University 1999, No.46, 36–43 (in Ukrainian).
[7] Dron’ V.S., Ivasyshen S.D. Properties of the volume potential for one class ultraparabolic equation of arbitrary order. Bukovinian Math. J. 2016, 4(3–4), 47–56 (in Ukrainian).
[8] Dron’ V.S., Ivasyshen S.D. On smoothness of volume potential for degenerate $\overrightarrow{2b}$-parabolic equations of Kolmogorov type. Nonclassical problems of the theory of differential equations: Call. of scientific works dedicated to 80-anniversary of B.Yo.Ptashnyk. IAPMM, Lviv, 2017, 38–53 (in Ukrainian).
[9] Ivasyshen S.D., Voznyak O.G. The Cauchy problem for parabolic systems with degeneration on the initial hypeplane. Dopovidi AN Ukrainy 1994, No.6, 7–11 (in Ukrainian).
[10] Ivasyshen S.D., Eidelman S.D. $\overrightarrow{2b}$-parabolic systems. Trudy Sem. Funkt. Anal. Kiev, Institute of Mathematics 1968, 1, 3–175, 271–273 (in Russian).
[11] Ivasyshen S.D., Medynsky I.P. On correct solvability of parabolic systems with degeneration on the initial hypeplane. Nauk. Visnyk Chernivtsi University 2000, No.76, 71–76 (in Ukrainian).
[12] Ivasyshen S.D., Medynsky I.P. Properties of integrals which have the type of derivatives of volume potentials for $\overrightarrow{2b}$-parabolic systems with degeneration on the initial hypeplane. Mat. Metody Fiz.-Mech. Polya 2002, 45(4), 76–86 (in Ukrainian).
[13] Ivasyshen S.D., Medynsky I.P. Cauchy problem for $\overrightarrow{2b}$-parabolic systems with degeneration on the initial
hypeplane. Mat. Metody Fiz.-Mech. Polya 2003, 46(3), 15–24 (in Ukrainian).
[14] Medynsky I.P. On a priori estimates for solutions of parabolic systems with degeneration on the initial hypeplane. Visnyk Nat. Univ. Lvivska Polytechnika 2000, No.407, 185–194 (in Ukrainian).

Cite
ACS Style
Dron’, V.; Medynsky, I. Properties of integrals which have the type of derivatives of volume potentials for degenerated $\overrightarrow{2b}$ -parabolic equation of Kolmogorov type. Bukovinian Mathematical Journal. 2021, 9 https://doi.org/https://doi.org/10.31861/bmj2021.02.01
AMA Style
Dron’ V, Medynsky I. Properties of integrals which have the type of derivatives of volume potentials for degenerated $\overrightarrow{2b}$ -parabolic equation of Kolmogorov type. Bukovinian Mathematical Journal. 2021; 9(2). https://doi.org/https://doi.org/10.31861/bmj2021.02.01
Chicago/Turabian Style
Vitaly Dron’, Igor Medynsky. 2021. "Properties of integrals which have the type of derivatives of volume potentials for degenerated $\overrightarrow{2b}$ -parabolic equation of Kolmogorov type". Bukovinian Mathematical Journal. 9 no. 2. https://doi.org/https://doi.org/10.31861/bmj2021.02.01
Export
We use own, third-party cookies, and localStorage files to analyze web traffic and page activities. Privacy Policy Settings