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arXiv · 1709.03931

Blow-up of solutions to semi-discrete parabolic-elliptic Keller-Segel models

Ansgar Jüngel·Oliver Leingang
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Abstract

The existence of weak solutions and upper bounds for the blow-up time for time-discrete parabolic-elliptic Keller-Segel models for chemotaxis in the two-dimensional whole space are proved. For various time discretizations, including the implicit Euler, BDF, and Runge-Kutta methods, the same bounds for the blow-up time as in the continuous case are derived by discrete versions of the virial argument. The theoretical results are illustrated by numerical simulations using an upwind finite-element method combined with second-order time discretizations.

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Ansgar Jüngel, Oliver Leingang. 2017-09-12. Blow-up of solutions to semi-discrete parabolic-elliptic Keller-Segel models. https://arxiv.org/abs/1709.03931

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