Properties of given and detected unbounded solutions to a class of chemotaxis models

TL;DR

This paper investigates unbounded solutions in chemotaxis models, identifying conditions for blow-up in various Lebesgue spaces, estimating blow-up times, and establishing criteria for blow-up in simplified models.

Contribution

It provides new insights into blow-up behavior in chemotaxis systems, including Lebesgue space analysis and blow-up criteria for simplified models.

Findings

Unbounded solutions blow up in specific Lebesgue spaces.

Estimates for blow-up times are derived.

Blow-up criteria are established for simplified models.

Abstract

This paper deals with unbounded solutions to a class of chemotaxis systems. In particular, for a rather general attraction-repulsion model, with nonlinear productions, diffusion, sensitivities and logistic term, we detect Lebesgue spaces where given unbounded solutions blow-up also in the corresponding norms of those spaces; subsequently, estimates for the blow-up time are established. Finally, for a simplified version of the model, some blow-up criteria are proved.