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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
Article

Abstract

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.

Keywords

Integral Representation Classical Solution Borel Measure Parabolic System Special Space 
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.

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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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