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arXiv · 1212.2807

Wellposedness and regularity for a degenerate parabolic equation arising in a model of chemotaxis with nonlinear sensitivity

Alexandre Montaru
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Abstract

We study a one-dimensional parabolic PDE with degenerate diffusion and non-Lipschitz nonlinearity involving the derivative. This evolution equation arises when searching radially symmetric solutions of a chemotaxis model of Patlak-Keller-Segel type. We prove its local in time wellposedness in some appropriate space, a blow-up alternative, regularity results and give an idea of the shape of solutions. A transformed and an approximate problem naturally appear in the way of the proof and are also crucial in [22] in order to study the global behaviour of solutions of the equation for a critical parameter, more precisely to show the existence of a critical mass.

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Alexandre Montaru. 2012-12-12. Wellposedness and regularity for a degenerate parabolic equation arising in a model of chemotaxis with nonlinear sensitivity. https://arxiv.org/abs/1212.2807

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