Global existence of solutions to a chemotaxis‐haptotaxis model with density‐dependent jump probability and quorum‐sensing mechanisms. (25th April 2018)

• Record Type: Journal Article
• Authors: Xu, Tianyuan; Ji, Shanming; Mei, Ming; Yin, Jingxue
• Other Names: Aristidou Andreas guestEditor.; Hildenbrand Dietmar guestEditor.; Staples George Stacey guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 41:Number 11(2018)
• Page Start: 4208
• Page End: 4226
• Publication Date: 2018-04-25
• Subjects: cancer invasion model -- chemotaxis -- global existence -- haptotaxis -- logistic source -- nonlinear diffusion; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4883
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, we first derive a new chemotaxis‐haptotaxis model of cancer invasion of tissue with density‐dependent jump probability and quorum‐sensing mechanisms, which is with degeneracy in diffusion. In the presence of generic logistic damping, we then prove the global existence of weak solutions. The approach adopted is the compactness analysis with Moser‐type iteration and artificial viscosity‐vanishing technique.