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Construction and estimation of fundamental matrices of solutions of polynomial coupling of $\vec {2b}$-elliptic systems generated by a $\vec {2b}$-parabolic system
Balabushenko Tonya Mykhailivna 1
1 Department of Mathematical Modeling, Yuriy Fedkovych Chernivtsi National University, Chernivtsi, 58000, Ukraine
Keywords: fundamental matrices of solutions, polynomial coupling, elliptic systems, parabolic system
Abstract

It was constructed and established estimates of fundamental matrices of solutions of polynomial sheaf of $\vec {2b}$-elliptic systems generated by stationary $\vec {2b}$-parabolic system which satisfies a special  $\Lambda ^{1, r}_δ$-condition.

References

[1] Eidelman S.D. Estimates of solutions of parabolic systems and their applications // Mat. sb. - 1953. - 33, N 2. - P. 359-382.

[2] Eidelman S.D. On the connection between the fundamental matrices of solutions of parabolic and elliptic systems / / Mat. sb. - 1954. - 35, N 1. - P.57-72.

[3] Eidelman S.D. On some properties of solutions of parabolic systems // Ukr. mat. zhurn. - 1956. - 8, N 2. - P.191-207.

[4] Eidelman S.D. Liouville theorems and theorems on stability for solutions of parabolic systems / / Mat. sb. - 1958. - 44, N 4. - P.481-508.

[5] Eidelman S.D. On fundamental solutions of parabolic systems. II // Mat. sb. - 1961.- 53, N 1. - P. 73-136.

[6] Eidelman S.D. Parabolic systems. - M.: Nauka, 1964.- 443 p.

[7] Ivasyshyn L.M. Investigation of qualitative properties of solutions of high-order parabolic systems in the time variable in the half-space $\mathbb{R}^{n+1}_+$ // Supplement of the NAS of Ukraine. - 1998. - N 1. - P.17-23.

[8] Balabushenko T.M. On estimates of Green matrix of the Cauchy problem for $\vec{2b}$-parabolic systems in unbounded with respect to time variable domains and their applications // Intern. Conf. " Nonlinear partial differential equations " (Kyiv, August 22-28, 2001): Book of abstracts. - Donetsk, 2001. - P.13.

[9] Balabushenko T.M. On estimates in unbounded domains with respect to the time variable of the fundamental matrix of solutions to the Cauchy problem for $\vec{2b}$-parabolic systems / / Mat. studii. - 2002. - 17, N 2. - P.163-174.

[10] Fedoryuk V.V. On the connection between the fundamental matrices of solutions of $\vec{2b}$-parabolic and $\vec{2b}$-elliptic systems // Abstracts of reports of the XX scientific session of ChSU. Section of mathematical sciences. - Chernivtsi, 1964.- P.52-53.

[11] Konenkov A.N. On the relationship between fundamental solutions of elliptic and parabolic equations / / Differential equations. - 2002. - 38, N 2. - P.247-256.

[12] Ivasyshen S.D., Kondur O.S. On the Green matrix of the Cauchy problem and the characterization of some classes of solutions for $\vec{2b}$-parabolic systems of arbitrary order // Mat. Studii. - 2000.- 14, N 1.- P.73-84.

Cite
ACS Style
Balabushenko, T.M. Construction and estimation of fundamental matrices of solutions of polynomial coupling of $\vec {2b}$-elliptic systems generated by a $\vec {2b}$-parabolic system. Bukovinian Mathematical Journal. 2018, 1
AMA Style
Balabushenko TM. Construction and estimation of fundamental matrices of solutions of polynomial coupling of $\vec {2b}$-elliptic systems generated by a $\vec {2b}$-parabolic system. Bukovinian Mathematical Journal. 2018; 1(160).
Chicago/Turabian Style
Tonya Mykhailivna Balabushenko. 2018. "Construction and estimation of fundamental matrices of solutions of polynomial coupling of $\vec {2b}$-elliptic systems generated by a $\vec {2b}$-parabolic system". Bukovinian Mathematical Journal. 1 no. 160.
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