come Trust (FC001204). N.V. acknowledges partial support from the ANR blanche project Kibord No ANR-13-BS01-0004 funded by the French Ministry of Research. Part of this work has been done while N.V. was a CNRS fellow at Imperial College, he is really grateful to the CNRS and to Imperial College for the opportunity of this visit. PD, SH and NV would like to thanks Jean-Paul Vincent for stimulating discussion.]{}

[**[Data Statement. ]{}** No new data were collected in the course of this research.]{}

[**[Keywords.]{}** Tissue growth; Two cell populations; Gradient flow; Incompressible limit; Free boundary problem]{}

[**[AMS subject classifications.]{}** 35K55; 35R35; 65M08; 92C15; 92C10]{}

Introduction
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Diversity is key in biology. It appears at all kind of level from the human scale to the microscopic scale, with million of cells types; each scales impacting on the others. During development, the coexistence of different cells types following different rules impact on the growth of tissue and then on the global structures. In a more specific case, this can be observed in cancerous tissue with the invasion of tumour cells in an healthy tissue creating a abnormal growth. Furthermore, cancerous cells are not playing all the same roles. They can be proliferative or 