On the global existence solution for a chemotaxis model

TL;DR

This paper proves that classical solutions to a complex chemotaxis PDE system remain bounded over time, establishing conditions for their global existence in a bounded domain.

Contribution

It demonstrates the global existence and boundedness of solutions for a complex chemotaxis model, extending previous local existence results.

Findings

Classical solutions are uniformly bounded in time.

Global existence of solutions is established under certain conditions.

The paper provides a priori estimates for the PDE system.

Abstract

This paper has been withdrawn by the authors. We consider the attraction-repulsion chemotaxis system (3 complicated PDEs system) under homogeneous Neumann boundary conditions in a bounded domain {\Omega} with smooth boundary, then the classical solutions to the system are uniformly-in-time bounded. After the local existence and uniqueness of solutions was proved, some priory estimates and proves will be established for the global existence of solutions (see the complete abstract in the PDF version of paper).