A diffusion model for cell polarization with interactions on the membrane

  • Yoshihisa MoritaEmail author
  • Kunimochi Sakamoto
Original Paper Area 1


We deal with a two-component system of linear diffusion equations in the bulk, under nonlinear interactions on the boundary. We give discussions on the existence and stability of equilibrium solutions. In particular, a stable non-uniform equilibrium solution is considered as representing a polarized state of a cell. Conditions for the stability of equilibrium solutions are given. To illustrate the results in concrete terms, we also analyze one dimensional problem in detail.


Diffusion system Nonlinear boundary value problem Linearized stability Bifurcations 

Mathematics Subject Classification

35B32 35B35 35J65 35K40 35J25 



The authors would like to thank the referees for useful comments for the revisions.


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Copyright information

© The JJIAM Publishing Committee and Springer Japan KK, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Applied Mathematics and InformaticsRyukoku UniversityOtsuJapan
  2. 2.Department of Mathematical and Life SciencesHiroshima UniversityHigashihiroshimaJapan

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