Global solutions for a supercritical drift-diffusion equation
- Author(s): Burczak, Jan
- Granero-Belinchón, Rafael
- et al.
Published Web Locationhttps://arxiv.org/pdf/1507.00694.pdf
We study the global existence of solutions to a one-dimensional drift-diffusion equation with logistic term, generalizing the classical parabolic-elliptic Keller-Segel aggregation equation arising in mathematical biology. In particular, we prove that there exists a global weak solution, if the order of the fractional diffusion $\alpha \in (1-c_1, 2]$, where $c_1>0$ is an explicit constant depending on the physical parameters present in the problem (chemosensitivity and strength of logistic damping). Furthermore, in the range $1-c_2<\alpha\leq 2$ with $0