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Izvestiya: Mathematics, 2006, Volume 70, Issue 2, Pages 233–263
DOI: https://doi.org/10.1070/IM2006v070n02ABEH002311 (Mi im555) 		 
This article is cited in 15 scientific papers (total in 15 papers)

Justification of the averaging method for parabolic equations containing rapidly oscillating terms with large amplitudes

V. B. Levenshtam

Rostov State University
English version PDF (470 kB) Citations (15)
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DOI: https://doi.org/10.1070/IM2006v070n02ABEH002311
Abstract: We justify the averaging method for abstract parabolic equations with stationary principal part that contain non-linearities (subordinate to the principal part) some of whose terms are rapidly oscillating in time with zero mean and are proportional to the square root of the frequency of oscillation. Our interest in the exponent 1/2 is motivated by the fact that terms proportional to lower powers of the frequency have no influence on the average. For linear equations of the same type, we justify an algorithm for the study of the stability of solutions in the case when the stationary averaged problem has eigenvalues on the imaginary axis (the critical case).
Received: 11.09.2003
Revised: 22.09.2004
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2006, Volume 70, Issue 2, Pages 25–56
DOI: https://doi.org/10.4213/im555
Bibliographic databases:
UDC: 517.43, 517.948, 513.881
MSC: 35R20, 35G05, 35K10
Language: English
Original paper language: Russian
Citation: V. B. Levenshtam, “Justification of the averaging method for parabolic equations containing rapidly oscillating terms with large amplitudes”, Izv. RAN. Ser. Mat., 70:2 (2006), 25–56; Izv. Math., 70:2 (2006), 233–263
Citation in format AMSBIB
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    • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:685
    Russian version PDF:305
    English version PDF:12
    References:59
    First page:3
     
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