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

Abstract

This 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.