Bifurcation analysis of nonlinear reaction-diffusion problems using wavelet-based reduction techniques

J. Krishnan; O. Runborg; I. G. Kevrekidis

doi:10.1016/j.compchemeng.2003.08.013

Bifurcation analysis of nonlinear reaction-diffusion problems using wavelet-based reduction techniques

J. Krishnan, O. Runborg, I. G. Kevrekidis

Chemical & Biological Engineering

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

Using a computational method for numerical homogenization, we perform the coarse-scale bifurcation analysis of nonlinear reaction-diffusion problems in both uniform and spatially varying media. The method is based on wavelet decomposition and projection of the differential equation on coarse scale wavelet spaces. The approach is capable of capturing turning points and pitchfork bifurcations of sharp, front-like solutions at the coarse level.

Original language	English (US)
Pages (from-to)	557-574
Number of pages	18
Journal	Computers and Chemical Engineering
Volume	28
Issue number	4
DOIs	https://doi.org/10.1016/j.compchemeng.2003.08.013
State	Published - Apr 15 2004

All Science Journal Classification (ASJC) codes

General Chemical Engineering
Computer Science Applications

Keywords

Bifurcation analysis
Numerical homogenization
Reaction-diffusion equations
Wavelets

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10.1016/j.compchemeng.2003.08.013

Cite this

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title = "Bifurcation analysis of nonlinear reaction-diffusion problems using wavelet-based reduction techniques",

abstract = "Using a computational method for numerical homogenization, we perform the coarse-scale bifurcation analysis of nonlinear reaction-diffusion problems in both uniform and spatially varying media. The method is based on wavelet decomposition and projection of the differential equation on coarse scale wavelet spaces. The approach is capable of capturing turning points and pitchfork bifurcations of sharp, front-like solutions at the coarse level.",

keywords = "Bifurcation analysis, Numerical homogenization, Reaction-diffusion equations, Wavelets",

author = "J. Krishnan and O. Runborg and Kevrekidis, {I. G.}",

note = "Funding Information: This work was partially supported by the National Science Foundation (through the KDI grant DMS-9872890) and a Humboldt For-schungs-preis to I.G.K. Extensive discussions with Dr. A. Gilbert (now at AT&T), on whose Thesis this work is based, as well as with Profs. I. Daubechies and B. Engquist are gratefully acknowledged. ",

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T1 - Bifurcation analysis of nonlinear reaction-diffusion problems using wavelet-based reduction techniques

AU - Krishnan, J.

AU - Runborg, O.

AU - Kevrekidis, I. G.

N1 - Funding Information: This work was partially supported by the National Science Foundation (through the KDI grant DMS-9872890) and a Humboldt For-schungs-preis to I.G.K. Extensive discussions with Dr. A. Gilbert (now at AT&T), on whose Thesis this work is based, as well as with Profs. I. Daubechies and B. Engquist are gratefully acknowledged.

PY - 2004/4/15

Y1 - 2004/4/15

N2 - Using a computational method for numerical homogenization, we perform the coarse-scale bifurcation analysis of nonlinear reaction-diffusion problems in both uniform and spatially varying media. The method is based on wavelet decomposition and projection of the differential equation on coarse scale wavelet spaces. The approach is capable of capturing turning points and pitchfork bifurcations of sharp, front-like solutions at the coarse level.

AB - Using a computational method for numerical homogenization, we perform the coarse-scale bifurcation analysis of nonlinear reaction-diffusion problems in both uniform and spatially varying media. The method is based on wavelet decomposition and projection of the differential equation on coarse scale wavelet spaces. The approach is capable of capturing turning points and pitchfork bifurcations of sharp, front-like solutions at the coarse level.

KW - Bifurcation analysis

KW - Numerical homogenization

KW - Reaction-diffusion equations

KW - Wavelets

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DO - 10.1016/j.compchemeng.2003.08.013

M3 - Article

AN - SCOPUS:1042301074

SN - 0098-1354

VL - 28

SP - 557

EP - 574

JO - Computers and Chemical Engineering

JF - Computers and Chemical Engineering

IS - 4

ER -

Bifurcation analysis of nonlinear reaction-diffusion problems using wavelet-based reduction techniques

Abstract

All Science Journal Classification (ASJC) codes

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