Mesenchymal Motion Models in One Dimension

: Mesenchymal motion denotes a form of cell movement through tissue, which can be observed for certain cancer metastasis. In [11], a mathematical model for this form of movement was introduced. In the current paper we present a comprehensive analysis of the one dimensional mesenchymal motion model. We establish the global existence of classical solutions and rigorously carry out the parabolic limit of the model. We discuss the stationary solutions, prove the existence of travelling wave solutions, and we use numerical simulations to illustrate the results. Finally, we discuss the biological implications of the results. Key words: Mesenchymal motion, pattern formation, global existence, macroscopic limits, traveling waves

• Type: Journal
• Year: 2008
• Where: SIAMAM
• Authors: Zhi-An Wang, Thomas Hillen, Michael Li
• Keywords: Global Existence, Mesenchymal Motion, Mesenchymal Motion Model, SIAMAM 2008