Nonlinear Reaction-Diffusion Processes for Nanocomposites: Anomalous Improved Homogenization

Jesús Ildefonso Díaz; David Gómez-Castro; Tatiana A. Shaposhnikova

Published by De Gruyter 2021

Nonlinear Reaction-Diffusion Processes for Nanocomposites

Anomalous Improved Homogenization

Jesús Ildefonso Díaz , David Gómez-Castro and Tatiana A. Shaposhnikova

Volume 39 in the series De Gruyter Series in Nonlinear Analysis and Applications

https://doi.org/10.1515/9783110648997

Overview
Contents

About this book

The behavior of materials at the nanoscale is a key aspect of modern nanoscience and nanotechnology. This book presents rigorous mathematical techniques showing that some very useful phenomenological properties which can be observed at the nanoscale in many nonlinear reaction-diffusion processes can be simulated and justified mathematically by means of homogenization processes when a certain critical scale is used in the corresponding framework.

An advanced monograph on reaction-diffusion processes for nanocomposites
Covers in detail all related techniques in anomalous homogenization
Of interest to researchers and graduate students in PDE's and applications

Author information

J. I. Díaz and D. Gómez-Castro, Complutense University of Madrid, Spain; T. A. Shaposhnikova, Lomonosov Moscow State University, Russia.

Topics

Frontmatter Publicly Available Download PDF	I
Preface Publicly Available Download PDF	VII
Notation Publicly Available Download PDF	IX
Contents Publicly Available Download PDF	XIII
1 Introduction and modeling Requires Authentication Unlicensed Licensed Download PDF	1
2 Preliminary results and comments Requires Authentication Unlicensed Licensed Download PDF	29
3 Estimates over one periodicity cell Requires Authentication Unlicensed Licensed Download PDF	43
4 Particles over the whole domain Requires Authentication Unlicensed Licensed Download PDF	69
5 Particles over an interior manifold Requires Authentication Unlicensed Licensed Download PDF	123
6 Particles over a part of the boundary Requires Authentication Unlicensed Licensed Download PDF	133
A Comments on the parabolic case Requires Authentication Unlicensed Licensed Download PDF	141
B Dynamic boundary condition Requires Authentication Unlicensed Licensed Download PDF	147
C Critical-size particles with a stochastic perturbation Requires Authentication Unlicensed Licensed Download PDF	157
Bibliography Requires Authentication Unlicensed Licensed Download PDF	165
Index Requires Authentication Unlicensed Licensed Download PDF	181

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Researchers and graduate students in partial differential equations and applied mathematics.
Pages
- Front matter: 16
- Main content: 184
Illustrations
- Illustrations: 5
- Tables: 3
Keywords: Homogenisierung; Mathematische Modellierung; Nanokomposit; Nichtlineare partielle Differentialgleichung; Reaktions-Diffusionsgleichung

eBook

Published: June 21, 2021
ISBN: 9783110648997

Hardcover

Published: June 21, 2021
ISBN: 9783110647273