On a singular limit as $$\theta \rightarrow 0$$ for a model for the evolution of morphogens in a growing tissue-Reference-Cited by-同舟云学术

On a singular limit as $$\theta \rightarrow 0$$ for a model for the evolution of morphogens in a growing tissue

Published:2023-04-20 Issue:3 Volume:74 Page:
ISSN:0044-2275
Container-title:Zeitschrift für angewandte Mathematik und Physik
language:en
Short-container-title:Z. Angew. Math. Phys.

Author:

Coclite G. M.,Coclite M.

Abstract

AbstractThis paper is devoted to the singular limit of a model for the regulation of growth and patterning in developing tissues by diffusing morphogens. The model is governed by a system of nonlinear PDEs. The arguments are based on energy estimates and a change of variable that reduces the system into a nonlinear PDE with singular diffusion.

Funder

Politecnico di Bari

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,General Physics and Astronomy,General Mathematics

Link

https://link.springer.com/content/pdf/10.1007/s00033-023-01993-z.pdf

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3. Coclite, G.M., Coclite, M.M.: On a model for the evolution of morphogens in a growing tissue II: $$\theta =\log (2)$$ case. Z. Angew. Math. Phys, 68(4)92, 20 (2017)

4. Coclite, G.M., Coclite, M.M.: On a model for the evolution of morphogens in growing tissue III: $$\theta <\log (2)$$. J. Differ. Equ. 263(2), 1079–1124 (2017)

5. Coclite, G.M., Coclite, M.M.: Long time behavior of a model for the evolution of morphogens in a growing tissue. Partial Differ. Equ. Appl., 1(1)4, 39 (2020)