In this work, we rigorously study chemotaxis effect versus haptotaxis effect on boundedness, blow-up and asymptotical behavior of solutions for a chemotaxis-haptotaxis model in 2D settings. It is well-known that the corresponding Keller–Segel chemotaxis-only model possesses a striking feature of critical mass blowup phenomenon, namely, subcritical mass ensures boundedness, whereas, supercritical mass induces the existence of blow-ups. Herein, we show that this critical mass blow-up phenomenon stays almost the same in the full chemotaxis-haptotaxis model and that any global-in-time haptotaxis solution component vanishes exponentially and the other two solution components converge exponentially to that of chemotaxis-only model in a global sense for suitably large chemo-sensitivity and in the usual sense for suitably small chemo-sensitivity. Therefore, haptotaixs is neither good nor bad than chemotaxis, showing negligibility of haptotaxis effect in the underlying chemotaxis-haptotaxis model.

中文翻译：

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趋化性 - 趋化性模型中趋化性效应的可忽略性

在这项工作中，我们严格研究趋化效应与趋化效应对 2D 设置中趋化性 - 趋化性模型的解的有界性、爆炸和渐近行为的影响。众所周知，相应的 Keller-Segel 趋化模型具有临界质量爆破现象的显着特征，即亚临界质量确保有界性，而超临界质量导致爆破的存在。在这里，我们表明，这种临界质量爆炸现象在完整的趋化性 - 趋化性模型中几乎保持不变，并且任何全局时间上的趋化性解决方案组件都呈指数消失，而其他两个解决方案组件以指数方式收敛到仅趋化性的解决方案组件全局意义上的模型适用于适当大的化学敏感性，而通常意义上的模型适用于适当小的化学敏感性。