科研之友
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摘要
Morphogen transport is a biological process, occurring in the tissue of living organisms, which is a determining step in cell differentiation. We present rigorous analysis of a simple model of this process, which is a system coupling parabolic PDE with ODE. We prove existence and uniqueness of solutions for both stationary and evolution problems. Moreover, we show that the solution converges exponentially to the equilibrium in C (1,alpha) x C (0,alpha) topology. We prove all results for arbitrary dimension of the domain. Our results improve significantly previously known results for the same model in the case of one-dimensional domain.
- 出版日期2012-6
