Abstract We study a free boundary problem modeling solid tumor growth with ECM and MDE interactions. The production rate of MDE by tumor cells is a nonlinear function depending on nutrients and MDE. This nonlinear term is more complicated. For this model, we can not give the explicit expressions or integral expressions for MDE terms while we only get the existence and uniqueness. At first, we show the existence and the uniqueness of radially symmetric stationary solutions. Then the existence of symmetry-breaking solutions bifurcating from the radially symmetric stationary solutions is obtained.

中文翻译：

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具有细胞外基质和基质降解酶的自由边界肿瘤模型的分叉

摘要 我们研究了一个自由边界问题，该问题通过 ECM 和 MDE 相互作用模拟实体瘤生长。肿瘤细胞产生 MDE 的速率是一个非线性函数，取决于营养物质和 MDE。这个非线性项更为复杂。对于这个模型，我们不能给出 MDE 项的显式表达式或积分表达式，而只能得到存在性和唯一性。首先，我们证明了径向对称平稳解的存在性和唯一性。然后得到了从径向对称平稳解分叉的对称破缺解的存在性。