Abstract
This work studies a triply haptotactic cross-diffusion system modeling oncolytic viral therapy, with interactions among uninfected cancer cells, extracellular matrix (ECM), infected cancer cells and oncolytic viruses (OV). In the recent paper (Tao and Winkler in J. Differ. Equ. 268:4973–4997, 2020), the authors asserted the global classical solvability in an oncolytic viral therapy model proposed by Alzahrani et al. (Math. Biosci. 310:76–95, 2019) with doubly haptotactic cross-diffusion terms in two-dimensional domain. In this continuous work, we take the ECM-OV taxis behavior into consideration and upgrade the model in Tao and Winkler (J. Differ. Equ. 268:4973–4997, 2020) to a triply haptotactic cross-diffusion system (also proposed in Alzahrani et al. in Math. Biosci. 310:76–95, 2019). It is rigorously proved that for all suitably regular initial data, an associated Neumann-type initial-boundary value problem for the spatially one-dimensional version of this model is globally solvable in the classical sense.
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Acknowledgements
This work is supported by the National Natural Science Foundation of China (Grant No. 11571020 and No. 11671021), and is also funded by China Scholarship Council. The author would like to thank the anonymous reviewers for many valuable comments and suggestions to improve the expressions.
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Tao, X. Global Classical Solutions to an Oncolytic Viral Therapy Model with Triply Haptotactic Terms. Acta Appl Math 171, 5 (2021). https://doi.org/10.1007/s10440-020-00375-1
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DOI: https://doi.org/10.1007/s10440-020-00375-1