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February  2004, 4(1): 337-348. doi: 10.3934/dcdsb.2004.4.337

A free boundary problem model of ductal carcinoma in situ

Yongzhi Xu 1,

1. 

Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, United States

Received  November 2002 Revised  June 2003 Published  November 2003

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.
Keywords: free boundary problem., ductal carcinoma in situ, Mathematical model.
Mathematics Subject Classification: 35R35, 35K5.
Citation: Yongzhi Xu. A free boundary problem model of ductal carcinoma in situ. Discrete and Continuous Dynamical Systems - B, 2004, 4 (1) : 337-348. doi: 10.3934/dcdsb.2004.4.337
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