On the global generalized solvability of a chemotaxis model with signal absorption and logistic growth terms

Abstract

Introducing a suitable solution concept, we show that in bounded smooth domains $\Omega \subset {\mathbb{R}}^n$, $n\ge 1$, the initial boundary value problem for the chemotaxis system \begin{align*} u_t&=Δu -χ\nabla\cdot\left(\frac{u}{v}\nabla v\right)+κu -μu^2,\\ v_t&=Δv -uv, \end{align*} with homogeneous Neumann boundary conditions and widely arbitrary initial data has a generalized global solution for any $\mu ,\kappa ,\chi >0$.

References in corpus (2)

• A new approach toward boundedness in a two-dimensional parabolic chemotaxis system with singular sensitivity
• Eventual smoothness of generalized solutions to a singular chemotaxis-Stokes system

Cited by in corpus (3)

• Chemotaxis(-fluid) systems with logarithmic sensitivity and slow consumption: global generalized solutions and eventual smoothness
• Strong convergence of weighted gradients in parabolic equations and applications to global generalized solvability of cross-diffusive systems
• Boundedness to a logistic chemotaxis system with singular sensitivity