We analyze a recently proposed model \cite{ABBM1}, for the regulation of growth and patterning in developing tissues by diffusing morphogens. We show that solutions of the underlying coupled systems of nonlinear PDEs exist, are unique and are stable in a suitable sense. The key tool in the analysis is the transformation of the underlying system to a porous medium equation. Numerical experiments, illustrating the model are also presented.
We analyze a recently proposed model \cite{ABBM1}, for the regulation of growth and patterning in developing tissues by diffusing morphogens. We show that solutions of the underlying coupled systems of nonlinear PDEs exist, are unique and are stable in a suitable sense. The key tool in the analysis is the transformation of the underlying system to a porous medium equation. Numerical experiments, illustrating the model are also presented.
On a model for the evolution of morphogens in a growing tissue
COCLITE, Giuseppe Maria;COCLITE, Mario;
2016-01-01
Abstract
We analyze a recently proposed model \cite{ABBM1}, for the regulation of growth and patterning in developing tissues by diffusing morphogens. We show that solutions of the underlying coupled systems of nonlinear PDEs exist, are unique and are stable in a suitable sense. The key tool in the analysis is the transformation of the underlying system to a porous medium equation. Numerical experiments, illustrating the model are also presented.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
