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2011, 2011(Special): 1344-1350. doi: 10.3934/proc.2011.2011.1344

Global bifurcation structure on a shadow system with a source term - Representation of all solutions-

Hideaki Takaichi 1, , Izumi Takagi 2, and  Shoji Yotsutani 3,

1. 

Information Media Center, Hyogo University, Hiraoka, Kakogawa, 675-0195, Japan
2. 

Tohoku University, Sendai, 980-8578, Japan
3. 

Department of Applied Mathematics and Informatics, Ryukoku University, Seta, Otsu 520-2194

Received  July 2010 Revised  April 2011 Published  October 2011

As the first step to understand the Gierer-Meinhardt system with source term, it is important to know the global bifurcation diagram of a shadow system. For the case without source term, it is well-understood. However, for the case with source term, the shadow system has a nonlocal term. Thus standard methods do not work, and there are a few partial results even for one-dimensional case. We give explicit representations of all solutions in terms of elliptic functions. They play crucial roles to clarify the global bifurcation diagram.
Keywords: parameter representation, reaction di usion, stationary.
Mathematics Subject Classification: 35J55.
Citation: Hideaki Takaichi, Izumi Takagi, Shoji Yotsutani. Global bifurcation structure on a shadow system with a source term - Representation of all solutions-. Conference Publications, 2011, 2011 (Special) : 1344-1350. doi: 10.3934/proc.2011.2011.1344
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