Dynamical Systems Weekend
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Plenary
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Abstract: The Poisson-Nernst-Planck (PNP) system serves as a basic model for electro-diffusion processes.In this talk, we will consider the dynamics of the PNP system as a model for in flows through membrane channels (a three dimensional tubular-like domain with two open ends).
We will start with a brief derivation of the PNP model. With a suitable interpretation of a common feature of biological channels, the three-dimensional PNP system will be reduced to a one-dimensional PNP system encoding the defining geometry of the three dimensional channel. For large Debye number, steady-states of the one-dimensional PNP system are studied from which important physiological information of the channel can be extracted. We will particularly discuss a new result on the multiplicity of steady-states as well as some physiological consequences.