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

Author

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  • Cao, Dingding
  • Li, Changpin
  • Zegeling, Paul Andries

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.

Suggested Citation

  • Cao, Dingding & Li, Changpin & Zegeling, Paul Andries, 2026. "Well-posedness and adaptive mesh FEM for the blow-up solution to the time-fractional Keller–Segel system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 249(C), pages 744-783.
    • Handle: RePEc:eee:matcom:v:249:y:2026:i:c:p:744-783
    DOI: 10.1016/j.matcom.2026.05.040
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