NDLI: Homogenization and concentrated capacity for the heat equation with non-linear variational data in reticular almost disconnected structures and applications to visual transduction

Please wait, while we are loading the content...

Homogenization and concentrated capacity for the heat equation with non-linear variational data in reticular almost disconnected structures and applications to visual transduction

Hyperbolic equations, function spaces with exponential weights and Nemytskij operators

Non-smooth atoms and pointwise multipliers in function spaces

Non-periodic isochronous oscillations in plane differential systems

Annali di Matematica Pura ed Applicata : Volume 182, Issue 3, August 2003

Annali di Matematica Pura ed Applicata : Volume 182, Issue 2, May 2003

Annali di Matematica Pura ed Applicata : Volume 182, Issue 1, April 2003

Annali di Matematica Pura ed Applicata : Volume 181

Annali di Matematica Pura ed Applicata : Volume 180

Annali di Matematica Pura ed Applicata : Volume 179

Annali di Matematica Pura ed Applicata : Volume 178

Annali di Matematica Pura ed Applicata : Volume 177

Annali di Matematica Pura ed Applicata : Volume 176

Annali di Matematica Pura ed Applicata : Volume 175

Annali di Matematica Pura ed Applicata : Volume 174

Annali di Matematica Pura ed Applicata : Volume 173

Annali di Matematica Pura ed Applicata : Volume 172

Homogenization and concentrated capacity for the heat equation with non-linear variational data in reticular almost disconnected structures and applications to visual transduction

Content Provider	Springer Nature Link
Author	Andreucci, D. Bisegna, P. DiBenedetto, E.
Copyright Year	2003
Abstract	Out of a right, circular cylinder Ωε of height H and cross-section a disc of radius R+σε one removes a stack of n≈H/ε parallel, equi-spaced cylinders C j , j=1,2,...,n, each of radius R and height νε. Here σ, ν are fixed positive numbers and ε is a positive parameter to be allowed to go to zero. The union of the C j almost fills Ωε in the sense that any two contiguous cylinders C j are at a mutual distance of the order of ε and that the outer shell, i.e., the gap S ε=Ωε-Ω o has thickness of the order of ε (Ω o is obtained from Ωε by formally setting ε=0). The cylinder Ωε from which the C j are removed, is an almost disconnected structure, it is denoted by Ωε, and it arises in the mathematical theory of phototransduction.For each ε>0 we consider the heat equation in the almost disconnected structure Ωε, for the unknown function u ε, with variational boundary data on the faces of the removed cylinders C j . The limit of this family of problems as ε→0 is computed by concentrating heat capacity and diffusivity on the outer shell, and by homogenizing the u ε within the limiting cylinder Ω o .It is shown that the limiting problem consists of an interior diffusion in Ω o and a boundary diffusion on the lateral boundary S of Ω o . The interior diffusion is governed by the 2-dimensional heat equation in Ω o , for an interior limiting function u. The boundary diffusion is governed by the Laplace–Beltrami heat equation on S, for a boundary limiting function u S . Moreover the exterior flux of the interior limit u provides the source term for the boundary diffusion on S. Finally the interior limit u, computed on S in the sense of the traces, coincides with the boundary limit u S . As a consequence of the geometry of Ωε, local arguments do not suffice to prove convergence in Ω o , and also we have to take into account the behavior of the solution in S ε. A key, novel idea consists in extending equi-bounded and equi-Hölder continuous functions in ε-dependent domains, into equi-bounded and equi-Hölder continuous functions in the whole ℝ N , by means of the Kirzbraun–Pucci extension technique.The biological origin of this problem is traced, and its application to signal transduction in the retina rod cells of vertebrates is discussed.
Starting Page	375
Ending Page	407
Page Count	33
File Format	PDF
ISSN	03733114
Journal	Annali di Matematica Pura ed Applicata
Volume Number	182
Issue Number	4
e-ISSN	16181891
Language	English
Publisher	Springer-Verlag
Publisher Date	2003-08-15
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	homogenization signal transduction concentration of capacity disconnected structure reticular structure
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Homogenization and concentrated capacity for the heat equation with non-linear variational data in reticular almost disconnected structures and applications to visual transduction

2003. Homogenization and concentrated capacity for the heat equation with nonlinear variational data in reticular almost disconnected structures and applications to visual transduction.

Équations aux dérivées partielles/partial differential equations homogenization and concentrated capacity in reticular almost disconnected structures (2002).

Homogenization and concentrated capacity for the heat equation with two kinds of microstructures: uniform cases

Data from: Multi-scale, numerical modeling of spatio-temporal signaling in cone phototransduction (Dataset)

Homogenization of Reynolds Equation by Two-Scale Convergence

Homogenization of a class of nonlinear variational inequalities with applications in fluid film flow

Non-parametric estimation in contaminated linear model

Integrability Condition on an Almost Complex Structure and Its Application

Homogenization and concentrated capacity for the heat equation with non-linear variational data in reticular almost disconnected structures and applications to visual transduction

Similar Documents

Homogenization and concentrated capacity for the heat equation with non-linear variational data in reticular almost disconnected structures and applications to visual transduction

2003. Homogenization and concentrated capacity for the heat equation with nonlinear variational data in reticular almost disconnected structures and applications to visual transduction.

Équations aux dérivées partielles/partial differential equations homogenization and concentrated capacity in reticular almost disconnected structures (2002).

Homogenization and concentrated capacity for the heat equation with two kinds of microstructures: uniform cases

Data from: Multi-scale, numerical modeling of spatio-temporal signaling in cone phototransduction (Dataset)

Homogenization of Reynolds Equation by Two-Scale Convergence

Homogenization of a class of nonlinear variational inequalities with applications in fluid film flow

Non-parametric estimation in contaminated linear model

Integrability Condition on an Almost Complex Structure and Its Application

Homogenization and concentrated capacity for the heat equation with non-linear variational data in reticular almost disconnected structures and applications to visual transduction