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中文摘要：
研究了一个时滞肿瘤生长自由边界问题，它来源于描述考虑了由于肿瘤细胞分裂速率变化引起肿瘤细胞生长环境的变化而引起的肿瘤细胞凋亡的肿瘤生长模型．在这个问题中考虑两种因素引起肿瘤细胞消亡：一种是肿瘤细胞度过固有的生命周期后自身的凋亡，另一种是肿瘤细胞的分裂速率变化引起生长环境的变化而引起的肿瘤细胞的凋亡，第二种消亡具有时滞．研究了该问题解的非负性，稳态解的存在唯一性和渐近性以及周期解的存在性．
英文摘要：
A free boundary problem modeling tumor growth with time delays is studied. The problem comes from the model of considering that the changes in proliferation rate can stimulate compensatory changes in apoptosis cell loss. In the problem, two parts that make apoptosis are considered： one is underlying apoptosis, the other is regulatory apoptosis with time delays. Nonnegativity of solutions, state stability, existence and uniqueness, asymptotical behavior of stable solutions, and existence of periodic solutions are studied.
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