Diffusion and cross-diffusion in pattern formation

Wei-Ming Ni

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2004)

  • Volume: 15, Issue: 3-4, page 197-214
  • ISSN: 1120-6330

Abstract

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We discuss the stability and instability properties of steady state solutions to single equations, shadow systems, as well as 2 × 2 systems. Our basic observation is that the more complicated the pattern are, the more unstable they tend to be.

How to cite

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Ni, Wei-Ming. "Diffusion and cross-diffusion in pattern formation." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 15.3-4 (2004): 197-214. <http://eudml.org/doc/252393>.

@article{Ni2004,
abstract = {We discuss the stability and instability properties of steady state solutions to single equations, shadow systems, as well as $2 \times 2$ systems. Our basic observation is that the more complicated the pattern are, the more unstable they tend to be.},
author = {Ni, Wei-Ming},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Diffusion; Cross-diffusion; Shadow systems; Steady states; Stability},
language = {eng},
month = {12},
number = {3-4},
pages = {197-214},
publisher = {Accademia Nazionale dei Lincei},
title = {Diffusion and cross-diffusion in pattern formation},
url = {http://eudml.org/doc/252393},
volume = {15},
year = {2004},
}

TY - JOUR
AU - Ni, Wei-Ming
TI - Diffusion and cross-diffusion in pattern formation
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2004/12//
PB - Accademia Nazionale dei Lincei
VL - 15
IS - 3-4
SP - 197
EP - 214
AB - We discuss the stability and instability properties of steady state solutions to single equations, shadow systems, as well as $2 \times 2$ systems. Our basic observation is that the more complicated the pattern are, the more unstable they tend to be.
LA - eng
KW - Diffusion; Cross-diffusion; Shadow systems; Steady states; Stability
UR - http://eudml.org/doc/252393
ER -

References

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