Existence and uniqueness of global classical solutions to a two dimensional two species cancer invasion haptotaxis model
We consider a haptotaxis cancer invasion model that includes two families of cancer cells. Both families migrate on the extracellular matrix and proliferate. Moreover the model describes an epithelial-to-mesenchymal-like transition between the two families, as well as a degradation and a self-recons...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2018
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| In: |
Discrete and continuous dynamical systems
Year: 2018, Volume: 23, Issue: 10, Pages: 4397-4431 |
| ISSN: | 1553-524X |
| DOI: | 10.3934/dcdsb.2018169 |
| Online Access: | Verlag, Volltext: https://dx.doi.org/10.3934/dcdsb.2018169
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| Author Notes: | Jan Giesselmann, Niklas Kolbe, Mária Lukáčová-Medvidová, and Nikolaos Sfakianakis |
| Summary: | We consider a haptotaxis cancer invasion model that includes two families of cancer cells. Both families migrate on the extracellular matrix and proliferate. Moreover the model describes an epithelial-to-mesenchymal-like transition between the two families, as well as a degradation and a self-reconstruction process of the extracellular matrix. We prove in two dimensional space positivity and conditional global existence and uniqueness of the classical solutions of the problem for large initial data. |
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| Item Description: | Gesehen am 08.04.2019 |
| Physical Description: | Online Resource |
| ISSN: | 1553-524X |
| DOI: | 10.3934/dcdsb.2018169 |