Uniform in time solutions for a chemotaxis with potential consumption model

Abstract

In this work we investigate the following chemo-attraction with consumption model in bounded domains of \, ${\mathbb{R}}^N$ ($N=1,2,3$): $${\partial }_{t}u-\Delta u=-\nabla \cdot (u\nabla v),{\partial }_{t}v-\Delta v=-u^{s}v$$ where $s\ge 1$, endowed with isolated boundary conditions and initial conditions for $(u,v)$. The main novelty in the model is the nonlinear potential consumption term $u^{s}v$. Through the convergence of solutions of an adequate truncated model, two main results are established; existence of uniform in time weak solutions in $3D$ domains, and uniqueness and regularity in $2D$ (or $1D$) domains. Both results are proved imposing minimal regularity assumptions on the boundary of the domain.

References in corpus (3)

• Global weak solutions in a three-dimensional chemotaxis-Navier-Stokes system
• Analysis of a chemotaxis model with indirect signal absorption
• Finite Element numerical schemes for a chemo-attraction and consumption model

Cited by in corpus (2)

• An optimal control problem subject to strong solutions of chemotaxis-consumption models
• Convergence of a time discrete scheme for a chemotaxis-consumption model