Journal
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
Volume 28, Issue 11, Pages 2211-2235Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218202518400134
Keywords
Chemotaxis; haptotaxis; tissue remodeling; cancer invasion; energy estimate
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Funding
- NUS AcRF Grant [R-146-000-249-114]
- NNSFC [11571363]
- Beijing Key Laboratory on MCAACI
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We consider a cancer invasion model comprising a strongly coupled PDE-ODE system in two and three space dimensions. The system consists of a parabolic equation describing cancer cell migration arising from a combination of chemotaxis and haptotaxis, a parabolic/elliptic equation describing the dynamics of matrix degrading enzymes (MDEs), and an ODE describing the evolution and re-modeling of the extracellular matrix (ECM). We point out that this strongly coupled PDE-ODE setup presents new mathematical difficulties, which are overcome by developing new integral estimate techniques. We prove that the system admits a unique global classical solution which is uniformly bounded in time in the two-dimensional spatial setting at all cancer cell proliferation rates. We also prove that, in the case of three-dimensional convex spatial domain, when cancer cell proliferation is suitably small, the system also possesses a unique classical solution for appropriately small initial data. These results improve previously known ones.
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