In this paper, we consider a nonlinear cancer invasion mathematical model with proliferation, growth and haptotaxis effects. We obtain lower bounds for the finite-time blow-up of solutions of the considered system with nonlinear diffusion operator when blow-up occurs. We have assumed both the Dirichlet and Neumann boundary conditions in \({\mathbb {R}}^n, n\ge 2\) to attain the desire result.

中文翻译：

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具有非线性扩散和触觉项的癌症入侵模型的爆发现象

在本文中，我们考虑具有扩散，生长和触觉效应的非线性癌症侵袭数学模型。当爆燃发生时，我们使用非线性扩散算子为所考虑系统的解的有限时间爆燃获得了下界。我们已经假设\（{\ mathbb {R}} ^ n，n \ ge 2 \）中的Dirichlet和Neumann边界条件都可以达到期望的结果。