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Volume 16, Issue 2
Global Coupling of an Interface Problem in an Activator-inhibitor System

YoonMee Ham

J. Part. Diff. Eq., 16 (2003), pp. 135-147.

Published online: 2003-05

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  • Abstract
An activator-inhibitor reaction system with global coupling was introduced in [1]. The authors showed that global coupling suppresses the breathing motion and enhances the propagation of the localized solution. The collision between two traveling waves for a sufficiently strong global coupling is discussed in [2]. If the width of layers is infinitesimally thin, the equation of motion for a pair of the interfaces is derived. We shall study the dynamics of interfaces in the free boundary problem with global coupling and with a strong global coupling.
  • Keywords

activator-inhibitor van der Pol equation global coupling free boundary problem Hopf bifurcation

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COPYRIGHT: © Global Science Press

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@Article{JPDE-16-135, author = {YoonMee Ham }, title = {Global Coupling of an Interface Problem in an Activator-inhibitor System}, journal = {Journal of Partial Differential Equations}, year = {2003}, volume = {16}, number = {2}, pages = {135--147}, abstract = { An activator-inhibitor reaction system with global coupling was introduced in [1]. The authors showed that global coupling suppresses the breathing motion and enhances the propagation of the localized solution. The collision between two traveling waves for a sufficiently strong global coupling is discussed in [2]. If the width of layers is infinitesimally thin, the equation of motion for a pair of the interfaces is derived. We shall study the dynamics of interfaces in the free boundary problem with global coupling and with a strong global coupling.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5412.html} }
TY - JOUR T1 - Global Coupling of an Interface Problem in an Activator-inhibitor System AU - YoonMee Ham JO - Journal of Partial Differential Equations VL - 2 SP - 135 EP - 147 PY - 2003 DA - 2003/05 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5412.html KW - activator-inhibitor KW - van der Pol equation KW - global coupling KW - free boundary problem KW - Hopf bifurcation AB - An activator-inhibitor reaction system with global coupling was introduced in [1]. The authors showed that global coupling suppresses the breathing motion and enhances the propagation of the localized solution. The collision between two traveling waves for a sufficiently strong global coupling is discussed in [2]. If the width of layers is infinitesimally thin, the equation of motion for a pair of the interfaces is derived. We shall study the dynamics of interfaces in the free boundary problem with global coupling and with a strong global coupling.
YoonMee Ham . (2003). Global Coupling of an Interface Problem in an Activator-inhibitor System. Journal of Partial Differential Equations. 16 (2). 135-147. doi:
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