Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Negligibility of haptotaxis effect in a chemotaxis-haptotaxis model   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.

5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph