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On a model for the evolution of morphogens in a growing tissue II: \(\varvec{\theta = \log (2)}\) case

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Abstract

We analyze a model for the regulation of growth and patterning in developing tissues by diffusing morphogens. We prove the well-posedness of the underlying systems of nonlinear PDEs. The key tool in the analysis is the transformation of the underlying system to an equation with singular logarithmic diffusion.

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Authors and Affiliations

  1. Department of Mechanics, Mathematics and Management, Polytechnic of Bari, via E. Orabona 4, 70125, Bari, Italy

    G. M. Coclite

  2. Department of Mathematics, University of Bari, via E. Orabona 4, 70125, Bari, Italy

    M. M. Coclite

Authors
  1. G. M. Coclite
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  2. M. M. Coclite
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Correspondence to G. M. Coclite.

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G. M. Coclite is member of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).

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Coclite, G.M., Coclite, M.M. On a model for the evolution of morphogens in a growing tissue II: \(\varvec{\theta = \log (2)}\) case. Z. Angew. Math. Phys. 68, 92 (2017). https://doi.org/10.1007/s00033-017-0838-0

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  • DOI: https://doi.org/10.1007/s00033-017-0838-0

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