Preprint: How do axolotl regrow lost limbs that match the size of the organism? A model of coupled morphogen dynamics & tissue growth suggests that some morphogen parameters should scale with animal size, but stay constant during regeneration, i.e. show static scaling https://www.biorxiv.org/content/10.1101/2025.02.14.638295v1
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Just for fun, here is a spherically-symmetric uniform-growth version of a static region of your single-morphogen model: https://visualpde.com/sim/?mini=lF74gzMx
and here is a dynamically-growing source region: https://visualpde.com/sim/?mini=mF__GsUq
I suspect coupling this to Turing dynamics would be fun.