<p>This study investigates an attraction–repulsion chemotaxis-consumption system with no-flux boundary condition and Dirichlet boundary conditions for signals on an open disc. Under the assumption that repulsion dominates attraction, we establish the existence of globally bounded radial classical solutions to the corresponding initial-boundary value problem for all nonnegative initial data possessing radial symmetry. Our results therefore demonstrate that the overbalancing of attraction by repulsion serves as a fundamental regularization mechanism for chemotaxis systems with Dirichlet boundary conditions for chemicals.</p>

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Global boundedness in an attraction–repulsion chemotaxis-consumption system with Dirichlet boundary conditions for signals

  • Gang Wang,
  • Taishan Yi

摘要

This study investigates an attraction–repulsion chemotaxis-consumption system with no-flux boundary condition and Dirichlet boundary conditions for signals on an open disc. Under the assumption that repulsion dominates attraction, we establish the existence of globally bounded radial classical solutions to the corresponding initial-boundary value problem for all nonnegative initial data possessing radial symmetry. Our results therefore demonstrate that the overbalancing of attraction by repulsion serves as a fundamental regularization mechanism for chemotaxis systems with Dirichlet boundary conditions for chemicals.