Change of homogenized absorption term in diffusion processes with reaction on the boundary of periodically distributed asymmetric particles of critical size

dc.contributor.authorDiaz, Jesus Ildefonso
dc.contributor.authorGomez-Castro, David
dc.contributor.authorShaposhnikova, Tatiana A.
dc.contributor.authorZubova, Maria
dc.date.accessioned2022-06-08T14:23:50Z
dc.date.available2022-06-08T14:23:50Z
dc.date.issued2017-07-13
dc.description.abstractThe main objective of this article is to get a complete characterization of the homogenized global absorption term, and to give a rigorous proof of the convergence, in a class of diffusion processes with a reaction on the boundary of periodically "microscopic" distributed particles (or holes) given through a nonlinear microscopic reaction (i.e. under nonlinear Robin microscopic boundary conditions). We introduce new techniques to deal with the case of non necessarily symmetric particles (or holes) of critical size which leads to important changes in the qualitative global homogenized reaction (such as it happens in many problems of the Nanotechnology). Here we shall merely assume that the particles (or holes) Gjε, in the n-dimensional space, are diffeomorphic to a ball (of diameter αε = C0εγ, γ = n/n-2 for some C0 > 0). To define the corresponding "new strange term" we introduce a one-parametric family of auxiliary external problems associated to canonical cellular problem associated to the prescribed asymmetric geometry G0 and the nonlinear microscopic boundary reaction σ(s) (which is assumed to be merely a Hölder continuous function). We construct the limit homogenized problem and prove that it is a well-posed global problem, showing also the rigorous convergence of solutions, as ε → 0, in suitable functional spaces. This improves many previous papers in the literature dealing with symmetric particles of critical size.
dc.description.departmentMathematics
dc.formatText
dc.format.extent25 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationDíaz, J. I., Gómez-Castro, D., Shaposhnikova, T. A., & Zubova, M. N. (2017). Change of homogenized absorption term in diffusion processes with reaction on the boundary of periodically distributed asymmetric particles of critical size. <i>Electronic Journal of Differential Equations, 2017</i>(178), pp. 1-25.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/15871
dc.language.isoen
dc.publisherTexas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.holderThis work is licensed under a Creative Commons Attribution 4.0 International License.
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2017, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectHomogenization
dc.subjectDiffusion processes
dc.subjectPeriodic asymmetric particles
dc.subjectMicroscopic non-linear boundary reaction
dc.subjectCritical sizes
dc.titleChange of homogenized absorption term in diffusion processes with reaction on the boundary of periodically distributed asymmetric particles of critical size
dc.typeArticle

Files

Original bundle

Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
diaz.pdf
Size:
337.61 KB
Format:
Adobe Portable Document Format
Description:

License bundle

Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
2.54 KB
Format:
Item-specific license agreed upon to submission
Description: