Critical cases of the degenrate drift-diffusion system

Takayoshi Ogawa
Tohoku University, Japan
15 March 2010, 3-4pm, Carslaw Room 273

Abstract

We consider the degenerate drift-diffusion system appearing in the semiconductor devise simulation, chemotaxis and the fluid mechanical approximation for the gravitational particles. There are some critical power appearing the degenerated term of the parabolic part of the system. I would like to show firstly how the system appears by the fluid mechanical approximation and then show the critical power in the system. One of them indeed corresponds the critical Sobolev exponent that is frequently appearing in the context of the semilinear heat equation.

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