LOCAL EXISTENCE OF A MULTI-SPECIES CHEMOTAXIS SYSTEM WITH MULTIPLE CHEMICALS AND LOGISTIC GROWTH

Kurt H. İ., Köroğlu T.

ASERC 4th INTERNATIONAL CONGRESS ON HEALTH, ENGINEERING, ARCHITECTURE and MATHEMATICS, Sankt-Peterburg, Russia, 23 - 29 July 2026, vol.1, no.1, pp.133-139, (Full Text)

  • Publication Type: Conference Paper / Full Text
  • Volume: 1
  • City: Sankt-Peterburg
  • Country: Russia
  • Page Numbers: pp.133-139
  • Karadeniz Technical University Affiliated: Yes

Abstract

This paper investigates a multi-species, multi-chemical chemotaxis system incorporating both cross-diffusion and nonlinear interaction effects over a bounded domain. The study focuses on the  local  existence,  uniqueness,  and  regularity  of  positive  classical  solutions.  Utilizing  the Banach  fixed-point  theorem  and  parabolic  regularity  theory,  it  is  established  that  the  system possesses  a  unique  classical  solution  on  a  maximal  existence  interval.  Furthermore, nonnegativity of the solutions is verified through the maximum principle.

Keywords:  Chemotaxis,  Cross-diffusion,  Local  existence,  Regularity,  Multi-species  system, Parabolic-elliptic PDEs.