Boundedness in a Two-Species Chemotaxis System with Nonlinear Resource Consumption

• Houzuo Ou ^[1] ; Liangchen Wang ^[1]
  1. [1] Chongqing University of Posts and Telecommunications

     Chongqing University of Posts and Telecommunications

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 1, 2024
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • This paper deals with a two-species chemotaxis system with nonlinear resource consumption ⎧ ⎪⎪⎨ ⎪⎪⎩ ut = u −∇· (u∇w) + μ1u(1 − u − a1v), x ∈ , t > 0, vt = v −∇· (v∇w) + μ2v(1 − a2u − v), x ∈ , t > 0, wt = w − (u + v)w (1 + u + v)θ , x ∈ , t > 0 under homogeneous Neumann boundary conditions in a smooth bounded domain ⊂ Rn(n ≥ 1), where the parameters μ1, μ2, a1, a2 > 0. For all suitably regular initial data, we prove that if θ > 0, the system possesses a unique global bounded classical solution.

• Referencias bibliográficas
  • 1. Baghaei, K., Khelghati, A.: Boundedness of classical solutions for a chemotaxis model with consumption of chemoattractant. C. R. Math....
  • 2. Bai, X., Winkler, M.: Equilibration in a fully parabolic two-species chemotaxis system with competitive kinetics. Indiana Univ. Math. J....
  • 3. Black, T.: Global generalized solutions to a forager-exploiter model with superlinear degradation and their eventual regularity properties....
  • 4. Black, T., Lankeit, J., Mizukami, M.: On the weakly competitive case in a two-species chemotaxis model. IMA J. Appl. Math. 81, 860–876...
  • 5. Chen, Y., Li, Z.: Asymptotic behavior in a forager-exploiter model with nonlinear resource consumption with/without general logistic sources....
  • 6. Fan, L., Jin, H.: Global existence and asymptotic behavior to a chemotaxis system with consumption of chemoattractant in higher dimensions....
  • 7. Fujie, K., Ito, A., Winkler, M., Yokota, T.: Stabilization in a chemotaxis model for tumor invasion. Discrete Contin. Dyn. Syst. 36, 151–169...
  • 8. Frassu, S., Viglialoro, G.: Boundedness criteria for a class of indirect (and direct) chemotaxisconsumption models in high dimensions....
  • 9. Horstmann, D., Winkler, M.: Boundedness vs. blow-up in a chemotaxis system. J. Differ. Equ. 215, 52–107 (2005)
  • 10. Keller, E.F., Segel, L.A.: Initiation of slime mold aggregation viewed as an instability. J. Theoret. Biol. 26, 399–415 (1970)
  • 11. Kowalczyk, R., Szyma ´nska, Z.: On the global existence of solutions to an aggregation model. J. Math. Anal. Appl. 343, 379–398 (2008)
  • 12. Lankeit, J., Wang, Y.: Global existence, boundedness and stabilization in a high-dimensional chemotaxis system with consumption. Discrete...
  • 13. Li, T., Suen, A., Winkler, M.: Global small-data solutions of a two-dimensional chemotaxis system with rotational flux terms. Math. Models...
  • 14. Li, X., Wang, L., Pan, X.: Boundedness and stabilization in the chemotaxis consumption model with signal-dependent motility. Z. Angew....
  • 15. Lin, K., Mu, C.: Convergence of global and bounded solutions of a two-species chemotaxis model with a logistic source. Discrete Contin....
  • 16. Lin, K., Mu, C., Wang, L.: Boundedness in a two-species chemotaxis system. Math. Methods Appl. Sci. 38, 5085–5096 (2015)
  • 17. Liu, Y., Zhuang, Y.: Boundedness in a high-dimensional forager-exploiter model with nonlinear resource consumption by two species. Z....
  • 18. Lv, W.: Global existence for a class of chemotaxis-consumption systems with signal dependent motility and generalized logistic source....
  • 19. Mizukami, M.: Boundedness and asymptotic stability in a two-species chemotaxis-competition model with signal-dependent sensitivity. Discrete...
  • 20. Mizukami, M.: Improvement of conditions for asymptotic stability in a two-species chemotaxiscompetition model with signal-dependent sensitivity....
  • 21. Murray, J.D.: Mathematical Biology. Springer, Berlin (1993)
  • 22. Ren, G., Liu, B.: Global existence and asymptotic behavior in a two-species chemo-taxis system with logistic source. J. Differ. Equ. 269,...
  • 23. Ren, G., Liu, B.: Global solvability and asymptotic behavior in a two-species chemotaxis system with Lotka–Volterra competitive kinetics....
  • 24. Tao, Y.: Boundedness in a chemotaxis model with oxygen consumption by bacteria. J. Math. Anal. Appl. 381, 521–529 (2011)
  • 25. Tao, Y., Winkler, M.: Energy-type estimates and global solvability in a two-dimensional chemotaxis– haptotaxis model with remodeling of...
  • 26. Tao, Y., Winkler, M.: Eventual smoothness and stabilization of large-data solutions in a threedimensional chemotaxis system with consumption...
  • 27. Tao, Y., Winkler, M.: Large time behavior in a forager-exploiter model with different taxis strategies for two groups in search of food....
  • 28. Tello, J.I., Winkler, M.: Stabilization in a two-species chemotaxis system with a logistic source. Nonlinearity 25, 1413–1425 (2012)
  • 29. Wang, J.: Global existence and boundedness of a forager-exploiter system with nonlinear diffusions. J. Differ. Equ. 276, 460–492 (2021)
  • 30. Wang, J.: Global existence and stabilization in a forager-exploiter model with general logistic sources. Nonlinear Anal. 222, 112985 (2022)
  • 31. Wang, J., Wang, M.: Global bounded solution of the higher-dimensional forager-exploiter model with/without growth sources. Math. Models...
  • 32. Wang, L., Mu, C.: A new result for boundedness and stabilization in a two-species chemotaxis system with two chemicals. Discrete Contin....
  • 33. Wang, L., Mu, C., Hu, X., Zheng, P.: Boundedness and asymptotic stability of solutions to a two-species chemotaxis system with consumption...
  • 34. Wang, L.,Mu, C., Hu, X.: Global solutions to a chemotaxis model with consumption of chemoattractant. Z. Angew. Math. Phys. 67, 96 (2016)
  • 35. Wang, L., Mu, C., Lin, K., Zhao, J.: Global existence to a higher-dimensional quasilinear chemotaxis system with consumption of chemoattractant....
  • 36. Wang, L., Mu, C., Zhou, S.: Boundedness in a parabolic-parabolic chemotaxis system with nonlinear diffusion. Z. Angew. Math. Phys. 65,...
  • 37. Wang, Y., Xiang, Z.: Global existence and boundedness in a higher-dimensional quasilinear chemotaxis system. Z. Angew. Math. Phys. 66,...
  • 38. Winkler, M.: Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model. J. Differ. Equ. 248, 2889–2905 (2010)
  • 39. Winkler, M.: Boundedness in the higher-dimensional parabolic-parabolic chemotaxis system with logistic source. Commun. Partial Differ....
  • 40. Winkler, M.: Global generalized solutions to a multi-dimensional doubly tactic resource consumption model accounting for social interactions....
  • 41. Winkler, M.: Global large-data solutions in a chemotaxis-(Navier-)Stokes system modeling cellular swimming in fluid drops. Commun. Partial...
  • 42. Winkler, M.: Large-data global generalized solutions in a chemotaxis system with tensor-valued sensitivities. SIAM J. Math. Anal. 47,...
  • 43. Wu, D., Shen, S.: Global boundedness and stabilization in a forager-exploiter model with logistic growth and nonlinear resource consumption....
  • 44. Xu, L., Mu, C., Xin, Q.: Global boundedness of solutions to the two-dimensional forager-exploiter model with logistic source. Discrete...
  • 45. Zhang, J., Hu, X., Wang, L., Qu, L.: Boundedness in a quasilinear two-species chemotaxis system with consumption of chemoattractant. Electron....
  • 46. Zhang, Q., Tao, W.: Boundedness and stabilization in a two-species chemotaxis system with signal absorption. Comput. Math. Appl. 78, 2672–2681...
  • 47. Zhang, Q., Li, Y.: Stabilization and convergence rate in a chemotaxis system with consumption of chemoattractant. J. Math. Phys. 56, 081506...
  • 48. Zheng, P., Mu, C.: Global boundedness in a two-competing-species chemotaxis system with two chemicals. Acta Appl. Math. 148, 157–177 (2017)