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Propagation fronts in a simplified model of tumor growth with degenerate cross-dependent self-diffusivity
Nonlinear Analysis: Real World Applications ( IF 1.8 ) Pub Date : 2021-08-05 , DOI: 10.1016/j.nonrwa.2021.103387
Thierry Gallay 1 , Corrado Mascia 2
Affiliation  

Motivated by tumor growth in Cancer Biology, we provide a complete analysis of existence and non-existence of invasive fronts for the reduced Gatenby–Gawlinski model tU=Uf(U)dV,tV=xf(U)xV+rVf(V),where f(u)=1u and the parameters d,r are positive. Denoting by (U,V) the traveling wave profile and by (U±,V±) its asymptotic states at ±, we investigate existence in the regimes d>1:(U,V)=(0,1)and(U+,V+)=(1,0),d<1:(U,V)=(1d,1)and(U+,V+)=(1,0),which are called, respectively, homogeneous invasion and heterogeneous invasion. In both cases, we prove that a propagating front exists whenever the speed parameter c is strictly positive. We also derive an accurate approximation of the front profile in the singular limit c0.



中文翻译:

具有退化交叉依赖性自扩散性的肿瘤生长简化模型中的传播前沿

受癌症生物学中肿瘤生长的驱动,我们为简化的 Gatenby-Gawlinski 模型提供了对侵袭前沿的存在和不存在的完整分析 =F()-d,=XF()X+rF(),在哪里 F()=1- 和参数 d,r是积极的。表示为(,) 行波剖面和由 (±,±) 它的渐近状态在 ±, 我们调查制度中的存在 d>1(-,-)=(0,1)(+,+)=(1,0),d<1(-,-)=(1-d,1)(+,+)=(1,0),分别称为同质入侵异质入侵。在这两种情况下,我们证明只要速度参数C是严格的正数。我们还推导出了奇异极限中前轮廓的准确近似值C0.

更新日期:2021-08-05
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