Ductal carcinoma in situ (DCIS) refers to a specific diagnosis of cancer
that is isolated within the breast duct, and has not spread to other
parts of the breast. We modify a model proposed by Byrne and Chaplain
for the growth of a tumour consisting of live cells (nonnecrotic tumour)
to describe the tumour growth inside a cylinder, a model mimicking
the growth of a ductal carcinoma. The model is in the form of a free
boundary problem. The analysis of stationary solutions of the problem
shows interesting results that are similar to the patterns found in DCIS.