Generalized Besicovitch spaces and applications to deterministic homogenization

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dc.contributor.author Sango, Mamadou
dc.contributor.author Svanstedt, Nils
dc.contributor.author Woukeng, Jean Louis
dc.date.accessioned 2012-05-29T08:41:58Z
dc.date.available 2012-05-29T08:41:58Z
dc.date.issued 2011-01
dc.description.abstract The purpose of the present work is to introduce a framework which enables us to study nonlinear homogenization problems. The starting point is the theory of algebras with mean value. Very often in physics, from very simple experimental data, one gets complicated structure phenomena. These phenomena are represented by functions which are permanent in mean, but complicated in detail. In addition the functions are subject to the verification of a functional equation which in general is nonlinear. The problem is therefore to give an interpretation of these phenomena using functions having the following qualitative properties: they are functions that represent a phenomenon on a large scale, and which vary irregularly, undergoing nonperiodic oscillations on a fine scale. In this work we study the qualitative properties of spaces of such functions, which we call generalized Besicovitch spaces, and we prove general compactness results related to these spaces. We then apply these results in order to study some new homogenization problems. One important achievement of this work is the resolution of the generalized weakly almost periodic homogenization problem for a nonlinear pseudo-monotone parabolic-type operator. We also give the answer to the question raised by Frid and Silva in their paper [35] [H. Frid, J. Silva, Homogenization of nonlinear pde’s in the Fourier–Stieltjes algebras, SIAM J. Math. Anal, 41 (4) (2009) 1589–1620] as regards whether there exist or do not exist ergodic algebras that are not subalgebras of the Fourier–Stieltjes algebra. en
dc.description.librarian nf2012 en
dc.description.sponsorship J.L. Woukeng acknowledges the support of the University of Pretoria through a postdoctoral fellowship. M. Sango and J.L. Woukeng are supported by a Focus Area Grant from the National Research Foundation of South Africa. en_US
dc.description.uri http://www.elsevier.com/locate/na en_US
dc.identifier.citation Mamadou Sango, Nils Svanstedt & Jean Louis Woukeng, Generalized Besicovitch spaces and applications to deterministic homogenization, Nonlinear Analysis: Theory, Methods & Applications, vol 74, no. 2, pp. 351-379, (2011), doi: 10.1016/j.na.2010.08.033 en
dc.identifier.issn 0362-546X (print)
dc.identifier.issn 1873-5215 (online)
dc.identifier.other 10.1016/j.na.2010.08.033
dc.identifier.uri http://hdl.handle.net/2263/18965
dc.language.iso en en_US
dc.publisher Elsevier en_US
dc.rights © 2010 Elsevier Ltd. All rights reserved. en_US
dc.subject Algebras with mean value en
dc.subject Generalized Besicovitch spaces en
dc.subject Weakly almost periodic functions en
dc.subject Pseudo-monotone operators en
dc.subject.lcsh Mean value theorems (Calculus) en
dc.subject.lcsh Homogenization (Differential equations) en
dc.title Generalized Besicovitch spaces and applications to deterministic homogenization en
dc.type Postprint Article en


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