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Izvestiya: Mathematics, 2009, Volume 73, Issue 6, Pages 1173–1196
DOI: https://doi.org/10.1070/IM2009v073n06ABEH002477 (Mi im2754) 		 
A boundary-value problem for a non-linear equation with a fractional derivative

E. I. Kaikinaab, P. I. Naumkinab, I. A. Shishmareva

a M. V. Lomonosov Moscow State University
b National Autonomous University of Mexico, Institute of Mathematics
English version PDF (340 kB) Russian version article
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DOI: https://doi.org/10.1070/IM2009v073n06ABEH002477
Abstract: We consider a problem on a half-line with a Neumann-type boundary condition. We prove the global existence of solutions and find the leading term of their large-time asymptotic expansion. The case of large initial data and critical non-linearity is considered in the case when the non-linear term of the equation decays in time as rapidly as the linear terms.
Keywords: Neumann-type boundary-value problem, non-linear equation, fractional derivative, asymptotic behaviour.
Received: 12.12.2007
Bibliographic databases:
UDC: 517.9+535.5
MSC: Primary 35Q55; Secondary 35A25, 35B40
Language: English
Original paper language: Russian
Citation: E. I. Kaikina, P. I. Naumkin, I. A. Shishmarev, “A boundary-value problem for a non-linear equation with a fractional derivative”, Izv. Math., 73:6 (2009), 1173–1196
Citation in format AMSBIB
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\by E.~I.~Kaikina, P.~I.~Naumkin, I.~A.~Shishmarev
\paper A~boundary-value problem for a~non-linear equation with a~fractional derivative
\jour Izv. Math.
\yr 2009
\vol 73
\issue 6
\pages 1173--1196
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  • https://www.mathnet.ru/eng/im/v73/i6/p101
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Russian version PDF:203
    English version PDF:13
    References:53
    First page:23
     
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