Ukrainian Mathematical Journal

, Volume 58, Issue 11, pp 1734–1747 | Cite as

Cauchy problem for parabolic systems with pulse action

  • M. I. Matiichuk
  • V. M. Luchko


For linear parabolic systems with pulse action, we establish the well-posedness of the Cauchy problem in normed Dini spaces.


Cauchy Problem Entire Function Parabolic System Fundamental Matrix Pulse Action 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. M. Samoilenko and N. A. Perestyuk, Impulsive Differential Equations [in Russian], Vyshcha Shkola, Kiev (1987).Google Scholar
  2. 2.
    S. D. Éidel’man, Parabolic Systems [in Russian], Nauka, Moscow (1964).Google Scholar
  3. 3.
    S. D. Ivasishen, Green Matrices of Parabolic Problems [in Russian], Vyshcha Shkola, Kiev (1990).zbMATHGoogle Scholar
  4. 4.
    O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural’tseva, Linear and Quasilinear Equations of Parabolic Type [in Russian], Nauka, Moscow (1967).Google Scholar
  5. 5.
    M. I. Matiichuk and S. D. Éidel’man, “On parabolic systems with Dini continuous coefficients,” Tr. Sem. Funkts. Anal., Voronezh, Issue 9, 51–83 (1967).Google Scholar
  6. 6.
    M. I. Matiichuk and S. D. Éidel’man, “Cauchy problem for parabolic systems whose coefficients have small smoothness,” Ukr. Mat. Zh., 22, No. 1, 22–36 (1970).CrossRefGoogle Scholar
  7. 7.
    M. I. Matiichuk, Parabolic Singular Boundary-Value Problems [in Ukrainian], Institute of Mathematics, Ukrainian Academy of Sciences, Kyiv (1999).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • M. I. Matiichuk
    • 1
  • V. M. Luchko
    • 1
  1. 1.Chernivtsi UniversityChernivtsi

Personalised recommendations