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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio

IMPACT FACTOR 2018: 0.551

CiteScore 2018: 0.52

SCImago Journal Rank (SJR) 2018: 0.320
Source Normalized Impact per Paper (SNIP) 2018: 0.711

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Volume 18, Issue 3


On nonclassical problems for first-order evolution equations

Gia Avalishvili
  • Faculty of Exact and Natural Sciences, I. Javakhishvili Tbilisi State University, 3 Chavchavadze Av., Tbilisi 0179, Georgia.
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/ Mariam Avalishvili
  • School of Mathematics and Information Technologies, University of Georgia, 77a M. Kostava St., Tbilisi 0175, Georgia.
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Published Online: 2011-07-14 | DOI: https://doi.org/10.1515/gmj.2011.0028


The present paper deals with nonclassical initial-boundary value problems for parabolic equations and systems and their generalizations in abstract spaces. Nonclassical problems with nonlocal initial conditions for an abstract first-order evolution equation with time-dependent operator are considered, the existence and uniqueness results are proved and the algorithm of approximation of nonlocal problems by a sequence of classical problems is constructed. Applications of the obtained general results to initial-boundary value problems for parabolic equations and systems are considered.

Keywords.: Abstract first-order evolution equations; parabolic equations and systems; non-local initial conditions; variational methods

About the article

Received: 2010-01-28

Published Online: 2011-07-14

Published in Print: 2011-09-01

Citation Information: Georgian Mathematical Journal, Volume 18, Issue 3, Pages 441–463, ISSN (Online) 1072-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj.2011.0028.

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