Dissipation Through Combinations of Nonlocal and Gradient Nonlinearities in Chemotaxis Models
Year: 2025
Type: article
Abstract: This work concerns with a class of chemotaxis models in which external sources, comprising nonlocal and gradient-dependent damping reactions, influence the motion of a cell density attracted by a chemical signal. The mechanism of the two densities is studied in bounded and impenetrable regions. In particular, it is seen that no gathering effect for the cells can appear in time provided that the damping impacts are sufficiently strong. Mathematically, we study this problem $$ \textstyle\begin{cases} u_{t}=\nabla \cdot \left ((u+1)^{m_{1}-1}\nabla u -\chi u(u+1)^{m_{2}-1} \nabla v\right )+ B(u,\nabla u)&{\mathrm{in}}\ \Omega \times \{t>0\} , \\ \tau v_{t}=\Delta v-v+f(u) &{\mathrm{in}}\ \Omega \times \{t>0\}, \\ u_{\nu }=v_{\nu }=0 &{\mathrm{on}}\ \partial \Omega \times \{t>0\}, \\ u(x, 0)=u_{0}(x), \tau v(x,0)= \tau v_{0}(x) &x \in \bar{\Omega }, \end{cases} $$ { u t = ∇ ⋅ ( ( u + 1 ) m 1 − 1 ∇ u − χ u ( u + 1 ) m 2 − 1 ∇ v ) + B ( u , ∇ u ) in Ω × { t > 0 } , τ v t = Δ v − v + f ( u ) in Ω × { t > 0 } , u ν = v ν = 0 on ∂ Ω × { t > 0 } , u ( x , 0 ) = u 0 ( x ) , τ v ( x , 0 ) = τ v 0 ( x )
Source: Acta Applicandae Mathematicae
Institution: University of Cagliari
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
Awards: G1100353153, G1191628478, G1511544777, G1865707705, G2023431758, G2107432758, G293126568, G3018935365, G311438708, G3824563768, G3859132754, G465505792, G4865800658, G5165036195, G5263057769, G5339074417, G5456286744, G5465607307, G5488169599, G5625038396, G5874873153, G620845374, G6333011530, G6350212530, G646276720, G658310711, G755372949, G832215605, G8568147916, G8803103535, G8820152341
OpenAlex ID: W4407363610