arXiv subjects

Mustafa Bazghandi

Publications and source records attributed to Mustafa Bazghandi.

3 recordsLinked to original sources

arXiv2026

Lie symmetry analysis of a 2+1-dimensional flux limited Keller Segel system

We investigate a two dimensional flux limited Keller Segel FLKS system using classical Lie symmetry analysis. The complete Lie point symmetry algebra is determined and shown to consist of temporal and spatial translations together with planar rotations. An optimal system of one-dimensional subalgebras is constructed, yielding stationary, translationally invariant, radially symmetric, travelling-wave, and rotatingwave reductions. The corresponding reduced equations are derived systematically. The results demonstrate that the flux limiting mechanism eliminates the scaling symmetries of the classical Keller Segel model and significantly restricts the class of admissible invariant solutions. Exact spatially homogeneous equilibrium solutions are determined, and integral representations for stationary radial and travelling-wave profiles are derived.

math.AP↗

arXiv2026

Similarity Solutions for the Flux limited Keller Segel System with Time Varying Chemical Decay Rate

We investigate a one dimensional flux limited Keller Segel system (FLKS) in which the chemical decay rate is allowed to vary explicitly in time, a feature motivated by enzymatic regulation and environmental variability in chemotactic signalling. Treating the decay rate as an arbitrary function, we carry out a systematic Lie symmetry analysis of the resulting PDE system and employ equivalence transformations to perform a complete group classification, we identify the kernel symmetry algebra admitted for arbitrary decay functions and determine three distinguished cases that extend the symmetry algebra constant decay rates, inverse time (power law) decay, and exponential decay. For each case, we construct an optimal system of subalgebras and derive the corresponding similarity reductions. Finally, we find some explicit solutions for our FLKS model. Our results provide a rigorous mathematical foundation for understanding which temporal decay patterns admit similarity reductions, thereby enabling analytical progress on flux limited chemotaxis models with realistic time varying degradation mechanisms.

math.AP↗

arXiv2025

Lie symmetry analysis and similarity reductions for the tempered-fractional Keller Segel system

We perform a Lie symmetry analysis on the tempered-fractional Keller Segel (TFKS) system, a chemo-taxis model incorporating anomalous diffusion. A novel approach is used to handle the nonlocal nature of tempered fractional operators. By deriving the full set of Lie point symmetries and identifying the optimal one-dimensional subalgebras, we reduce the TFKS PDEs to ordinary differential equations (ODEs), yielding new exact solutions. These results offer insights into the long-term behavior and aggregation dynamics of the TFKS model and present a methodology applicable to other tempered fractional differential equations.

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