Global existence of solutions to a chemotaxis-haptotaxis model with density-dependent jump probability and quorum-sensing mechanisms. (English) Zbl 1397.92105
Summary: 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.
MSC:
| 92C17 | Cell movement (chemotaxis, etc.) |
| 92C50 | Medical applications (general) |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
Keywords:
cancer invasion model; chemotaxis; global existence; haptotaxis; logistic source; nonlinear diffusionReferences:
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