Cauchy problem for a class of parabolic systems of Shilov type with variable coefficients

• Autorzy: Vladyslav Litovchenko , Iryna Dovzhytska
• Języki publikacji: EN

Abstrakty

EN

In the case of initial data belonging to a wide class of functions including distributions of Gelfand-Shilov type we establish the correct solvability of the Cauchy problem for a new class of Shilov parabolic systems of equations with partial derivatives with bounded smooth variable lower coefficients and nonnegative genus. We also investigate the conditions of local improvement of the convergence of a solution of this problem to its limiting value when the time variable tends to zero.

Słowa kluczowe

EN

Cauchy problem; Shilov parabolic systems with variable coefficients; Generalized initial data; Correct solvability; Principle of localization

Kategorie tematyczne

• 35K46: Initial value problems for higher-order parabolic systems
• 35K41: Higher-order parabolic systems
• 35B30: Dependence of solutions on initial and boundary data, parameters
• 35A08: Fundamental solutions
• 35D99: None of the above, but in this section

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 3
• Strony: 1084-1102

Daty

wydano

2012-06-01

online

2012-03-24

Twórcy

autor

Vladyslav Litovchenko

• Yu. Fedkovych Chernivtsi National University,

autor

Iryna Dovzhytska

• Yu. Fedkovych Chernivtsi National University,

Bibliografia

• [1] Gel’fand I.M., Shilov G.E., Generalized Functions. 3, Academic Press, New York-London, 1967
• [2] Gel’fand I.M., Shilov G.E. Generalized Functions. 2, Academic Press, New York-London, 1968
• [3] Gorodetskii V.V., Localization principle for solutions of the Cauchy problem for parabolic systems in the class of generalized functions of infinite order, Differ. Uravn., 1985, 21(6), 1077–1079 (in Russian)
• [4] Khou-sin’ U., On the definition of parabolic systems of partial differential equations, Uspekhi Mat. Nauk, 1960, 15(6), 157–161 (in Russian)
• [5] Litovchenko V.A., Dovzhitska I.M., The fundamental matrix of solutions of the Cauchy problem for a class of parabolic systems of the Shilov type with variable coefficients, J. Math. Sci., 2011, 175(4), 450–476 http://dx.doi.org/10.1007/s10958-011-0356-0
• [6] Zhitomirskii Ya.I., The Cauchy problem for certain types of systems, parabolic in the sense of G.E. Shilov, of linear partial differential equations with variable coefficients, Izv. Akad. Nauk SSSR Ser. Mat., 1959, 23, 925–932 (in Russian)

Identyfikatory

DOI

10.2478/s11533-012-0025-7