论文标题
在趋化性热模型中触觉效应的可忽略
Negligibility of haptotaxis effect in a chemotaxis-haptotaxis model
论文作者
论文摘要
在这项工作中，我们严格研究趋化性效应与触觉效应对2D设置中合并趋化性智术模型的解决方案的界限，爆炸和渐近行为的影响。众所周知，相应的Keller-segel趋化模型具有关键质量爆炸现象的引人注目的特征，即，亚临界质量可确保界限，而超临界质量会引起爆炸的存在。本文中，我们表明，在完整的趋化性haptotaxis模型中，这种临界质量爆炸现象几乎保持不变。为了忽略触觉对渐近行为的验证，我们表明，随着时间的变化接近无限，任何全球范围内的触觉溶液组件都会呈指数式消失，而其他两个解决方案组件则与全球含义上的趋化性模型呈指数融合，从而使全球含义的模型具有适当的大型化学意义，并且在本质上具有适当的化学意义上的化学意义上的小型化学效果。因此，即使在任意引入抗触觉的情况下，上述仅趋化模型的临界质量爆炸现象也几乎是未被发现的，与趋化性效应相比，在界限，趋化性和长期行为方面，触觉效应的效果可忽略不计。
In this work, we rigorously study chemotaxis effect versus haptotaxis effect on boundedness, blow-up and asymptotical behavior of solutions for a combined 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 blow-up 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. For negligibility of haptotaxis on asymptotical behavior, we show that any global-in-time haptotaxis solution component vanishes exponentially as time approaches infinity, 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, the aforementioned critical mass blow-up phenomenon for the chemotaxis-only model is almost undestroyed even with arbitrary introduction of haptotaixs, showing negligibility of haptotaxis effect compared to chemotaxis effect in terms of boundedness, blow-up and longtime behavior in the chemotaxis-haptotaxis model.
