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On a nonlinear parabolic problem arising in the quantum diffusive description of a degenerate fermion gas

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If you have a question about this talk, please contact Harsha Hutridurga .

In this talk we consider, both theoretically and numerically, a nonlinear drift-diffusion equation describing a gas of fermions in the zero-temperature limit. The equation is defined in a bounded domain whose boundary is divided into an “insulating” part, where homogeneous Neumann conditions are imposed, and a “contact” part, where nonhomogeneous Dirichlet data are assigned. The existence of stationary solutions for a suitable class of Dirichlet data is proven by assuming a simple domain configuration. The long-time behavior of the time-dependent solution, for more complex domain configurations, is investigated by means of numerical experiments.

This talk is part of the Geometric Analysis & Partial Differential Equations seminar series.

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