A diffusion model for cell polarization with interactions on the membrane
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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.
KeywordsDiffusion system Nonlinear boundary value problem Linearized stability Bifurcations
Mathematics Subject Classification35B32 35B35 35J65 35K40 35J25
The authors would like to thank the referees for useful comments for the revisions.
- 12.LaSalle, J., Lefschetz, S.: Stability by Liapunov’s Direct Methods with Applications. Academic Press, New York (1961)Google Scholar