Ukrainian Mathematical Journal

, Volume 42, Issue 4, pp 443–448 | Cite as

Integral representation and initial values of solutions of 2\(\overrightarrow b\)-parabolic systems

  • S. D. Ivasishen


Necessary and sufficient conditions are found under which the classical solutions of 2\(\overrightarrow b\)-parabolic systems, defined in a halfopen layer, can be represented as the Poisson integrals of functions or generalized Borel measures from the special spaces Lpk(0,a), 1 < p ≤ ∞, or Mk(0,a). It is elucidated as to in what sense the solutions, representable by Poisson integrals, satsfy the initial conditions.


Integral Representation Classical Solution Borel Measure Parabolic System Special Space 
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Literature cited

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    S. D. Éidel'man, Parabolic Systems [in Russian], Nauka, Moscow (1964).Google Scholar
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    S. D. Ivasishen and S. D. Éidel'man, “The 2\(\overrightarrow b\)-parabolic systems,” in: Proceedings of the Seminar on Functional Analysis [in Russian], No. 1, Inst. Mat. Akad. Nauk UkrSSR, Kiev (1968), pp. 3–175.Google Scholar
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    J. Chabrowski, “Representation theorems for parabolic systems,” J. Austral. Math. Soc.,A32, No. 2, 246–288 (1982).Google Scholar
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    S. D. Ivasishen, “On integral representations and Fatou's property for solutions of parabolic systems,” Usp. Mat. Nauk,41, No. 4, 173–174 (1986).Google Scholar

Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • S. D. Ivasishen
    • 1
  1. 1.Kiev UniversityUSSR

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