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Mathematical analysis of a tumor invasion model—global existence and stability
Nonlinear Analysis: Real World Applications ( IF 2 ) Pub Date : 2021-03-30 , DOI: 10.1016/j.nonrwa.2021.103297
Xueyan Tao , Yuanwei Qi , Shulin Zhou

This work studies an outstanding reaction–diffusion system modeling tumor invasion, with interactions among tumor tissue, acid concentration and normal tissue. This model has very different features from the models extensively studied in the mathematics literature. The most challenge issue for mathematical analysis of the present model is the existence of classical solution, since the diffusion of tumor tissue is influenced by the density of normal cells and diffusion degeneracy arises when normal cells are at the carrying capacity. A rigorous proof of global existence and uniqueness of classical solutions is presented. Moreover, we study global dynamics of the solution, and show asymptotic stability of the four possible constant equilibria under various scenarios.



中文翻译:

肿瘤入侵模型的数学分析-整体存在性和稳定性

这项工作研究了一个出色的反应扩散系统,该系统模拟了肿瘤的侵袭,并在肿瘤组织,酸浓度和正常组织之间相互作用。该模型与数学文献中广泛研究的模型有很大不同。当前模型的数学分析面临的最大挑战是经典解决方案的存在,因为肿瘤组织的扩散受正常细胞密度的影响,而扩散变性则在正常细胞处于载量时出现。给出了经典解的全局存在性和唯一性的严格证明。此外,我们研究了解的整体动力学,并显示了在各种情况下四个可能的恒定平衡点的渐近稳定性。

更新日期:2021-03-30
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