Global existence of solutions to a parabolic-elliptic chemotaxis system with critical degenerate di ffusion

Elissar Nasreddine

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arXiv · 1207.4453

Global existence of solutions to a parabolic-elliptic chemotaxis system with critical degenerate di ffusion

Elissar Nasreddine

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Abstract

This paper is devoted to the analysis of non-negative solutions for a degenerate parabolic-elliptic Patlak-Keller-Segel system with critical nonlinear diffusion in a bounded domain with homogeneous Neumann boundary conditions. Our aim is to prove the existence of a global weak solution under a smallness condition on the mass of the initial data, there by completing previous results on nite blow-up for large masses. Under some higher regularity condition on solutions, the uniqueness of solutions is proved by using a classical duality technique.

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Elissar Nasreddine. 2012-07-18. Global existence of solutions to a parabolic-elliptic chemotaxis system with critical degenerate di ffusion. https://arxiv.org/abs/1207.4453

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