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Russian Mathematical Surveys, 2014, Volume 69, Issue 3, Pages 419–433
DOI: https://doi.org/10.1070/RM2014v069n03ABEH004897 (Mi rm9591) 		 
This article is cited in 11 scientific papers (total in 11 papers)

An explicit Lyapunov function for reflection symmetric parabolic partial differential equations on the circle

B. Fiedlera, C. Grotta-Ragazzob, C. Rochac

a Institut für Mathematik, Freie Universität Berlin, Berlin, Germany
b Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo, Brazil
c Instituto Superior Técnico, Lisboa, Portugal
English version PDF (501 kB) Citations (11)
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DOI: https://doi.org/10.1070/RM2014v069n03ABEH004897
Abstract: An explicit Lyapunov function is constructed for scalar parabolic reaction-advection-diffusion equations under periodic boundary conditions. The non-linearity is assumed to be even with respect to the advection term. The method followed was originally suggested by H. Matano for, and limited to, separated boundary conditions.
Bibliography: 20 titles.
Keywords: partial differential equations, variational methods, convection, energy functional, advection, reaction-diffusion equations, periodic boundary conditions.
Funding agency Grant number
Deutsche Forschungsgemeinschaft SFB 647
Fundação para a Ciência e a Tecnologia
National Council for Scientific and Technological Development (CNPq) 305089/2009-9
B. Fiedler and C. Rocha were partially supported by the Deutsche Forschungsgemeinschaft, SFB 647 Space–Time–Matter, and by FCT Portugal. C. Grotta-Ragazzo was partially supported by CNPq Grant no. 305089/2009-9, Brazil.
Received: 25.10.2013
Russian version:
Uspekhi Matematicheskikh Nauk, 2014, Volume 69, Issue 3(417), Pages 27–42
DOI: https://doi.org/10.4213/rm9591
Bibliographic databases:
Document Type: Article
UDC: 517.956.4
MSC: 35B40, 35K55
Language: English
Original paper language: Russian
Citation: B. Fiedler, C. Grotta-Ragazzo, C. Rocha, “An explicit Lyapunov function for reflection symmetric parabolic partial differential equations on the circle”, Uspekhi Mat. Nauk, 69:3(417) (2014), 27–42; Russian Math. Surveys, 69:3 (2014), 419–433
Citation in format AMSBIB
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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:62
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