Existence and uniqueness of global classical solutions to a two dimensional two species cancer invasion haptotaxis model

• Verfasst von: Giesselmann, Jan [VerfasserIn]
• Verfasst von: Sfakianakis, Nikolaos [VerfasserIn]
• Titel: Existence and uniqueness of global classical solutions to a two dimensional two species cancer invasion haptotaxis model
• Verf.angabe: Jan Giesselmann, Niklas Kolbe, Mária Lukáčová-Medvidová, and Nikolaos Sfakianakis
• Jahr: 2018
• Umfang: 35 S.
• Fussnoten: Gesehen am 08.04.2019
• Titel Quelle: Enthalten in: Discrete and continuous dynamical systems / B
• Ort Quelle: Springfield, Mo. : American Institute of Mathematical Sciences, 2001
• Jahr Quelle: 2018
• Band/Heft Quelle: 23(2018), 10, Seite 4397-4431
• ISSN Quelle: 1553-524X
• DOI: doi:10.3934/dcdsb.2018169
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1662933622

Abstract

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.