References

  1. Shilov G.E. On conditions of correctness of Cauchy’s problem for systems of partial differential equations with constant coefficients. Uspekhi Mat. Nauk 1955, 10 (4), 89–100. (in Russian)
  2. Petrovskii I.G. On the Cauchy problem for systems of equations with partial derivatives in a domain of nonanalytic functions. Bull. Mosk. Gos. Univ. Ser. Mat. Mekh. 1938, 1 (7), 1–72. (in Russian)
  3. Gel’fand I., Shilov G. Generalized functions. Vol. 3. Theory of differential equations. Academic Press, New York, 1967.
  4. Eidelman S.D., Ivasishen S.D., Porper F.O. The Liouville theorems for systems parabolic by Shilov. Izv. Vyssh. Uchebn. Zaved. Mat. 1961, 6, 169–179. (in Russian)
  5. 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)
  6. Boroc V.M. Reduction of a system of linear equations in partial derivatives with constant coefficients to the canonical canonical form. Dokl. Akad. Nauk SSSR 1957, 115 (1), 13–16. (in Russian)
  7. Litovchenko V. The Cauchy problem for Shilov parabolic equations. Sib. Math. J. 2004, 45 (4), 669–679. doi:10.1023/B:SIMJ.0000035831.63036.bb (translation of Sibirsk. Mat. Zh. 2004, 45 (4), 809–821. (in Russian))
  8. Litovchenko V. Cauchy problem for \(\{\overrightarrow{\vphantom{h}p};\overrightarrow{h}\}\)-parabolic equations with time-dependent coefficients. Math. Notes 2005, 77 (3–4), 364–379. doi:10.1007/s11006-005-0036-9
  9. Kostić M. Shilov parabolic systems. Bull. Cl. Sci. Math. Nat. Sci. Math. 2012, 37, 19–39.
  10. Hou-Sin U. On the definition of parabolic systems of partial differential equations. Uspekhi Mat. Nauk 1960, 15 (6), 157–161. (in Russian)
  11. Zhitomirskii Ya.I. Cauchy problem for some types of systems of linear equations, which are parabolic by G.E. Shilov, with partial derivatives with continuous coefficients. Izv. Akad. Nauk SSSR Ser. Mat. 1959, 23, 925–932. (in Russian)
  12. Litovchenko V., Dovzhytska I. Cauchy problem for a class of parabolic systems of Shilov type with variable coefficients. Cent. Eur. J. Math. 2012, 10 (3), 1084–1102. doi:10.2478/s11533-012-0025-7
  13. Litovchenko V.A., Unguryan G.M. Conjugate Cauchy problem for parabolic Shilov type systems with nonnegative genus. Differ. Equ. 2018, 54 (3), 335–351. doi:10.1134/S0012266118030060 (translation of Differ. Uravn. 2018, 54 (3), 341–357. (in Russian))
  14. Litovchenko V., Unguryan G. Some properties of Green’s functions of Shilov-type parabolic systems. Miskolc Math. Notes 2019, 20 (1), 365–379. doi:10.18514/MMN.2019.2089
  15. Schwartz L. Théorie des distributions. Hermann, Paris, 1966.
  16. Gel’fand I.M., Shilov G.E. Spaces of fundamental and generalized functions. Fizmatlit, Moscow, 1958. (in Russian)
  17. Kashpirovsky A.I. Equality of the spaces \(S_\alpha^\beta\) and \(S_\alpha\cap S^\beta\). Funct. Anal. Appl. 1980, 14 (2), 129–129. doi:10.1007/BF01086561 (translation of Funkts. Anal. Prilozh. 1980, 14 (2), 60–60. (in Russian))
  18. Eidelman S.D. Parabolic systems. North-Holland, Amsterdam, 1969.
  19. Friedman A. Partial differential equations of parabolic type. Prentice-Hall, Englewood Cliffs, 1964.