Negligibility of haptotaxis effect in a chemotaxis-haptotaxis model

作者：Jin, Hai-Yang; Xiang, Tian^*

来源：Mathematical Models and Methods in Applied Sciences, 2021, 31(07): 1373-1417.

DOI：10.1142/S0218202521500287

• Chemotaxis-haptotaxis
• negligibility of haptotaxis
• global existence
• boundedness
• blow-up

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.