Well-posedness and adaptive mesh FEM for the blow-up solution to the time-fractional Keller–Segel system

Dingding Cao, Changpin Li and Paul Andries Zegeling

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 249, issue C, 744-783

Abstract: This paper deals with well-posedness and blow-up of Caputo–Hadamard time-fractional Keller–Segel system. In order to enhance the simulation of the blow-up solution, two adaptive mesh methods are proposed, where the intrinsic characteristics of solutions to single-point and multi-point two-dimensional blow-up problems are incorporated. By constructing auxiliary functions and employing moving mesh strategies, adaptive meshes can be pre-generated and adjusted. Numerical experiments show the effectiveness of the methods.

Keywords: Caputo–Hadamard derivative; Keller–Segel system; Blow-up; Adaptive mesh method; Moving mesh; Fractional chemotaxis system (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:249:y:2026:i:c:p:744-783

DOI: 10.1016/j.matcom.2026.05.040

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