American Institute of Mathematical Sciences

Advanced
  • Previous Article
    On the stabilization of a flexible structure via a nonlinear delayed boundary control
  • DCDS-B Home
  • This Issue
  • Next Article
    The existence and properties of the solution of a class of nonlinear differential equations with switching at variable times
doi: 10.3934/dcdsb.2021273
Online First

Online First articles are published articles within a journal that have not yet been assigned to a formal issue. This means they do not yet have a volume number, issue number, or page numbers assigned to them, however, they can still be found and cited using their DOI (Digital Object Identifier). Online First publication benefits the research community by making new scientific discoveries known as quickly as possible.

Readers can access Online First articles via the “Online First” tab for the selected journal.

Global generalized solutions to the forager-exploiter model with logistic growth

Qian Zhao 1,2, and  Bin Liu 1,2,,

1. 

School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, China
2. 

Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, China

* Corresponding author: Bin Liu

Received  July 2021 Revised  September 2021 Early access November 2021

Fund Project: This work is supported by National Natural Science Foundation of China grant 11971185

This paper presents the global existence of the generalized solutions for the forager-exploiter model with logistic growth under appropriate regularity assumption on the initial value. This result partially generalizes previously known ones.

Keywords: Chemotaxis, forager-exploiter model, global existence, generalized solution.
Mathematics Subject Classification: Primary: 35D30; Secondary: 35A01, 35Q92.
Citation: Qian Zhao, Bin Liu. Global generalized solutions to the forager-exploiter model with logistic growth. Discrete and Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2021273
References:
[1]

H. Amann, Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems. In Function spaces, differential operators and nonlinear analysis, Function Spaces, Differential Operators and Nonlinear Analysis, 133 (1993), 9-126.  doi: 10.1007/978-3-663-11336-2_1.

[2]

N. Bellomo, A. Bellouquid, Y. Tao and M. Winkler, Toward a mathematical theory of Keller-Segel models of pattern formation in biological tissues, Math. Models Methods Appl. Sci., 25 (2015), 1663-1763.  doi: 10.1142/S021820251550044X.

[3]

N. Bellomo and J. Soler, On the mathematical theory of the dynamics of swarms viewed as complex systems, Math. Models Methods Appl. Sci., 22 (2012), 1140006.  doi: 10.1142/s0218202511400069.

[4]

T. Black, Global generalized solutions to a forager-exploiter model with superlinear degradation and their eventual regularity properties, Math. Mod. Meth. Appl. Sci., 30 (2020), 1075-1117.  doi: 10.1142/S0218202520400072.

[5]

X. Bai and M. Winkler, Equilibrium in a fully parabolic two-species chemotaxis system with competitive kinetics, Indiana Univ. Math. J., 65 (2016), 553-583.  doi: 10.1512/iumj.2016.65.5776.

[6]

F. Dai and B. Liu, Asymptotic stability in a quasilinear chemotaxis-haptotaxis model with general logistic source and nonlinear signal production, J. Differential Equations, 269 (2020), 10839-10918.  doi: 10.1016/j.jde.2020.07.027.

[7]

R. Eftimie, G. de Verirs and M. A. Lewis, Complex spatial group patterns result from different animal communication mechanisms, Proc. Natl. Acad. Sci. USA, 104 (2007), 6974-6979.  doi: 10.1073/pnas.0611483104.

[8]

G. Furioli, A. Pulvirenti, E. Terraneo and G. Toscani, Fokker-Planck equations in the modeling of socio-economic phenomena, Math. Mod. Meth. Appl. Sci., 27 (2017), 115-158.  doi: 10.1142/S0218202517400048.

[9]

S. Fu and L. Miao, Global existence and asymptotic stability in a predator-prey chemotaxis model, Nonlinear Anal. RWA., 54 (2020), 103079.  doi: 10.1016/j.nonrwa.2019.103079.

[10]

M. A. Herrero and J. J. L. Velazquez, A blow-up mechanism for a chemotaxis model, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 24 (1997), 633-683. 

[11]

W. Hoffman, D. Heinemann and J. A. Wiens, The ecology of seabird feeding flocks in Alaska, The Auk, 98 (1981), 437-456. 

[12]

H. Y. Jin and Z. A. Wang, Global stability of prey-taxis system, J. Differential Equations, 262 (2017), 1257-1290.  doi: 10.1016/j.jde.2016.10.010.

[13]

E. Keller and L. Segel, Initiation of slime mold aggregation viewed as an instability, J. Theoret. Biol., 26 (1970), 399-415.  doi: 10.1016/0022-5193(70)90092-5.

[14]

K. Lin and C. Mu, Convergence of global and bounded solutions of a two-species chemotaxis model with a logistic source, Discrete Contin. Dyn. Syst., Ser. B, 22 (2017), 2233-2260.  doi: 10.3934/dcdsb.2017094.

[15]

K. Lin, C. Mu and L. Wang, Boundedness in a two-species chemotaxis system, Math. Methods Appl. Sci., 38 (2015), 5085-5096.  doi: 10.1002/mma.3429.

[16]

K. Lin, C. Mu and H. Zhong, A new approach toward stabilization in a two-species chemotaxis model with logistic source, Comput. Math. Appl., 75 (2018), 837-849.  doi: 10.1016/j.camwa.2017.10.007.

[17]

K. Lin and T. Xiang, On boundedness, blow-up and convergence in a two-species and two-stimuli chemotaxis system with$\setminus$without loop, Calc. Var. Partial Equations, 59 (2020), 35pp. doi: 10.1007/s00526-020-01777-7.

[18]

Y. Liu, Global existence and boundedness of classical solutions to a forager-exploiter model with volume-filling effects, Nonlinear Anal. Real World Appl., 50 (2019), 519-531.  doi: 10.1016/j.nonrwa.2019.05.015.

[19]

M. Mizukami, Boundedness and asymptotic stability in a two-species chemotaxis-competition model with signal-dependent sensitivity, Discrete Contin. Dyn. Syst., Ser. B, 22 (2017), 2301-2319.  doi: 10.3934/dcdsb.2017097.

[20]

T. Nagai T. Senb and K. Yoshida, Application of the Trudinger-Moser inequality to a parabolic system of chemotaxis, Funkcial. Ekvac., 40 (1997), 411-433. 

[21]

K. Osaki and A. Yagi, Finite dimensional attractor for one-dimensional Keller-Segel equations, Funkcial. Ekvac., 44 (2001), 441-469. 

[22]

G. Ren, Boundedness and stabilization in a two-species chemotaxis system with logistic source, Z. Angew. Math. Phys., 71 (2020), 177, 17pp. doi: 10.1007/s00033-020-01410-9.

[23]

G. Ren and B. Liu, Global existence and asymptotic behavior in a two-species chemotaxis system with logistic source, J. Differential Equations, 269 (2020), 1484-1520.  doi: 10.1016/j.jde.2020.01.008.

[24]

G. Ren and B. Liu, Global boundedness and asymptotic behavior in a quasilinear attraction-repulsion chemotaxis model with nonlinear signal production and logistic-type source, Math. Models Methods Appl. Sci., 30 (2020), 2619-2689.  doi: 10.1142/S0218202520500517.

[25]

G. Ren and B. Liu, Global solvability and asymptotic behavior in a two-species chemotaxis system with Lotka-Volterra competitive kinetics, Math. Models Methods Appl. Sci., 31 (2021), 941-978.  doi: 10.1142/S0218202521500238.

[26]

C. Stinner, J. I. Tello and M. Winkler, Competitive exclusion in a two-species chemotaxis model, J. Math. Biol., 68 (2014), 1607-1626.  doi: 10.1007/s00285-013-0681-7.

[27]

M. B. Short, M. R. D'Orsogna, V. B. Pasour, G. E. Tita, P. J. Brantingham, A. L. Bertozzi and L. B. Chayes, A statistical model of criminal behavior, Math. Models Methods Appl. Sci., 18 (2008), 1249-1267.  doi: 10.1142/S0218202508003029.

[28]

N. Sfakianakis, N. Kolbe, N. Hellmann and M. Lukáčová-Medvid'ová, Large time behavior in a forager-exploiter model with different taxis strategies for two groups in search of food, Math. Models Methods Appl. Sci., 29 (2019), 2151-2182. 

[29]

J. Toner and Y. Tu, Flocks, herds, and schools: A quantitative theory of flocking, Phys. Rev. E, 58 (1998), 4828-4858.  doi: 10.1103/PhysRevE.58.4828.

[30]

N. Tania, B. Vanderlei, J. P. Heath and L. Edelstein-Keshet, Role of social interactions in dunamic patterns of resource pathches and forager aggregation, Proc. Natl. Acad. Sci. U.S.A., 109 (2012), 11228-11233.  doi: 10.1073/pnas.1201739109.

[31]

G. Viglialoro, Very weak global solutions to a parabolic-parabolic chemotaxis-system with logistic source, J. Math. Anal. Appl., 439 (2016), 197-212.  doi: 10.1016/j.jmaa.2016.02.069.

[32]

J. Wang and M. Wang, Global bounded solution of the higher-dimensional forager-exploiter model with/without growth sources, Math. Models Methods Appl. Sci., 30 (2020), 1297-1323.  doi: 10.1142/S0218202520500232.

[33]

L. Wang, J. Zhang, C. Mu and X. Hu, Boundedness and stabilization in a two-species chemotaxis system with two chemicals, Discrete Contin. Dyn. Syst. Ser. B, 25 (2020), 191-221. 

[34]

M. Winkler, Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model, J. Differential Equations, 248 (2010), 2889-2905.  doi: 10.1016/j.jde.2010.02.008.

[35]

M. Winkler, Boundedness and stabilization in a multi-dimensional chemotaxis-haptotaxis model, Mathématique, 141 (2020), 583-624. 

[36]

M. Winkler, Boundedness in the high-dimensional parabolic-parabolic chemotaxis system with strong logistic dampening, J. Differential Equations, 257 (2014), 1056-1077.  doi: 10.1016/j.jde.2014.04.023.

[37]

M. Winkler, Global generalized solutions to a multi-dimensional doubly tactic resource consumption model accounting for social interactions, Math. Models Methods Appl. Sci., 29 (2019), 373-418.  doi: 10.1142/S021820251950012X.

[38]

M. Winkler, Large-data global generalized solution in a chemotaxis system with tensor-valued sensitivities, SIAM J. Math. Anal., 47 (2015), 3029-3115.  doi: 10.1137/140979708.

[39]

M. Winkler, Small-mass solution in the two-dimensionsl Keller-Segel system coupled to the Navier-Stokes equations, SIAM J. Math. Anal., 52 (2020), 2041-2080.  doi: 10.1137/19M1264199.

[40]

M. Winkler, $L^1$ solutions to parabolic Keller-Segel systems involving arbitrary superlinear degradation, preprint.

[41]

M. Winker, Global boundedness of solutions on the two-dimensional forager-exploiter model with logistic source, Discrete Contin. Dyn. Syst. Ser., 41 (2021), 3031-3043. 

[42]

T. Xiang, Chemotactic aggregation versus logistic damping on boundedness in the 3D minimal Keller-Segel Model, SIAM J. Appl. Math., 78 (2018), 2420-2438.  doi: 10.1137/17M1150475.

[43]

Q. Zhang and Y. Li, Global boundedness of solutions to a two-species chemotaxis system, Z. Angew. Math. Mech., 66 (2015), 83-93.  doi: 10.1007/s00033-013-0383-4.

show all references

References:
[1]

H. Amann, Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems. In Function spaces, differential operators and nonlinear analysis, Function Spaces, Differential Operators and Nonlinear Analysis, 133 (1993), 9-126.  doi: 10.1007/978-3-663-11336-2_1.

[2]

N. Bellomo, A. Bellouquid, Y. Tao and M. Winkler, Toward a mathematical theory of Keller-Segel models of pattern formation in biological tissues, Math. Models Methods Appl. Sci., 25 (2015), 1663-1763.  doi: 10.1142/S021820251550044X.

[3]

N. Bellomo and J. Soler, On the mathematical theory of the dynamics of swarms viewed as complex systems, Math. Models Methods Appl. Sci., 22 (2012), 1140006.  doi: 10.1142/s0218202511400069.

[4]

T. Black, Global generalized solutions to a forager-exploiter model with superlinear degradation and their eventual regularity properties, Math. Mod. Meth. Appl. Sci., 30 (2020), 1075-1117.  doi: 10.1142/S0218202520400072.

[5]

X. Bai and M. Winkler, Equilibrium in a fully parabolic two-species chemotaxis system with competitive kinetics, Indiana Univ. Math. J., 65 (2016), 553-583.  doi: 10.1512/iumj.2016.65.5776.

[6]

F. Dai and B. Liu, Asymptotic stability in a quasilinear chemotaxis-haptotaxis model with general logistic source and nonlinear signal production, J. Differential Equations, 269 (2020), 10839-10918.  doi: 10.1016/j.jde.2020.07.027.

[7]

R. Eftimie, G. de Verirs and M. A. Lewis, Complex spatial group patterns result from different animal communication mechanisms, Proc. Natl. Acad. Sci. USA, 104 (2007), 6974-6979.  doi: 10.1073/pnas.0611483104.

[8]

G. Furioli, A. Pulvirenti, E. Terraneo and G. Toscani, Fokker-Planck equations in the modeling of socio-economic phenomena, Math. Mod. Meth. Appl. Sci., 27 (2017), 115-158.  doi: 10.1142/S0218202517400048.

[9]

S. Fu and L. Miao, Global existence and asymptotic stability in a predator-prey chemotaxis model, Nonlinear Anal. RWA., 54 (2020), 103079.  doi: 10.1016/j.nonrwa.2019.103079.

[10]

M. A. Herrero and J. J. L. Velazquez, A blow-up mechanism for a chemotaxis model, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 24 (1997), 633-683. 

[11]

W. Hoffman, D. Heinemann and J. A. Wiens, The ecology of seabird feeding flocks in Alaska, The Auk, 98 (1981), 437-456. 

[12]

H. Y. Jin and Z. A. Wang, Global stability of prey-taxis system, J. Differential Equations, 262 (2017), 1257-1290.  doi: 10.1016/j.jde.2016.10.010.

[13]

E. Keller and L. Segel, Initiation of slime mold aggregation viewed as an instability, J. Theoret. Biol., 26 (1970), 399-415.  doi: 10.1016/0022-5193(70)90092-5.

[14]

K. Lin and C. Mu, Convergence of global and bounded solutions of a two-species chemotaxis model with a logistic source, Discrete Contin. Dyn. Syst., Ser. B, 22 (2017), 2233-2260.  doi: 10.3934/dcdsb.2017094.

[15]

K. Lin, C. Mu and L. Wang, Boundedness in a two-species chemotaxis system, Math. Methods Appl. Sci., 38 (2015), 5085-5096.  doi: 10.1002/mma.3429.

[16]

K. Lin, C. Mu and H. Zhong, A new approach toward stabilization in a two-species chemotaxis model with logistic source, Comput. Math. Appl., 75 (2018), 837-849.  doi: 10.1016/j.camwa.2017.10.007.

[17]

K. Lin and T. Xiang, On boundedness, blow-up and convergence in a two-species and two-stimuli chemotaxis system with$\setminus$without loop, Calc. Var. Partial Equations, 59 (2020), 35pp. doi: 10.1007/s00526-020-01777-7.

[18]

Y. Liu, Global existence and boundedness of classical solutions to a forager-exploiter model with volume-filling effects, Nonlinear Anal. Real World Appl., 50 (2019), 519-531.  doi: 10.1016/j.nonrwa.2019.05.015.

[19]

M. Mizukami, Boundedness and asymptotic stability in a two-species chemotaxis-competition model with signal-dependent sensitivity, Discrete Contin. Dyn. Syst., Ser. B, 22 (2017), 2301-2319.  doi: 10.3934/dcdsb.2017097.

[20]

T. Nagai T. Senb and K. Yoshida, Application of the Trudinger-Moser inequality to a parabolic system of chemotaxis, Funkcial. Ekvac., 40 (1997), 411-433. 

[21]

K. Osaki and A. Yagi, Finite dimensional attractor for one-dimensional Keller-Segel equations, Funkcial. Ekvac., 44 (2001), 441-469. 

[22]

G. Ren, Boundedness and stabilization in a two-species chemotaxis system with logistic source, Z. Angew. Math. Phys., 71 (2020), 177, 17pp. doi: 10.1007/s00033-020-01410-9.

[23]

G. Ren and B. Liu, Global existence and asymptotic behavior in a two-species chemotaxis system with logistic source, J. Differential Equations, 269 (2020), 1484-1520.  doi: 10.1016/j.jde.2020.01.008.

[24]

G. Ren and B. Liu, Global boundedness and asymptotic behavior in a quasilinear attraction-repulsion chemotaxis model with nonlinear signal production and logistic-type source, Math. Models Methods Appl. Sci., 30 (2020), 2619-2689.  doi: 10.1142/S0218202520500517.

[25]

G. Ren and B. Liu, Global solvability and asymptotic behavior in a two-species chemotaxis system with Lotka-Volterra competitive kinetics, Math. Models Methods Appl. Sci., 31 (2021), 941-978.  doi: 10.1142/S0218202521500238.

[26]

C. Stinner, J. I. Tello and M. Winkler, Competitive exclusion in a two-species chemotaxis model, J. Math. Biol., 68 (2014), 1607-1626.  doi: 10.1007/s00285-013-0681-7.

[27]

M. B. Short, M. R. D'Orsogna, V. B. Pasour, G. E. Tita, P. J. Brantingham, A. L. Bertozzi and L. B. Chayes, A statistical model of criminal behavior, Math. Models Methods Appl. Sci., 18 (2008), 1249-1267.  doi: 10.1142/S0218202508003029.

[28]

N. Sfakianakis, N. Kolbe, N. Hellmann and M. Lukáčová-Medvid'ová, Large time behavior in a forager-exploiter model with different taxis strategies for two groups in search of food, Math. Models Methods Appl. Sci., 29 (2019), 2151-2182. 

[29]

J. Toner and Y. Tu, Flocks, herds, and schools: A quantitative theory of flocking, Phys. Rev. E, 58 (1998), 4828-4858.  doi: 10.1103/PhysRevE.58.4828.

[30]

N. Tania, B. Vanderlei, J. P. Heath and L. Edelstein-Keshet, Role of social interactions in dunamic patterns of resource pathches and forager aggregation, Proc. Natl. Acad. Sci. U.S.A., 109 (2012), 11228-11233.  doi: 10.1073/pnas.1201739109.

[31]

G. Viglialoro, Very weak global solutions to a parabolic-parabolic chemotaxis-system with logistic source, J. Math. Anal. Appl., 439 (2016), 197-212.  doi: 10.1016/j.jmaa.2016.02.069.

[32]

J. Wang and M. Wang, Global bounded solution of the higher-dimensional forager-exploiter model with/without growth sources, Math. Models Methods Appl. Sci., 30 (2020), 1297-1323.  doi: 10.1142/S0218202520500232.

[33]

L. Wang, J. Zhang, C. Mu and X. Hu, Boundedness and stabilization in a two-species chemotaxis system with two chemicals, Discrete Contin. Dyn. Syst. Ser. B, 25 (2020), 191-221. 

[34]

M. Winkler, Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model, J. Differential Equations, 248 (2010), 2889-2905.  doi: 10.1016/j.jde.2010.02.008.

[35]

M. Winkler, Boundedness and stabilization in a multi-dimensional chemotaxis-haptotaxis model, Mathématique, 141 (2020), 583-624. 

[36]

M. Winkler, Boundedness in the high-dimensional parabolic-parabolic chemotaxis system with strong logistic dampening, J. Differential Equations, 257 (2014), 1056-1077.  doi: 10.1016/j.jde.2014.04.023.

[37]

M. Winkler, Global generalized solutions to a multi-dimensional doubly tactic resource consumption model accounting for social interactions, Math. Models Methods Appl. Sci., 29 (2019), 373-418.  doi: 10.1142/S021820251950012X.

[38]

M. Winkler, Large-data global generalized solution in a chemotaxis system with tensor-valued sensitivities, SIAM J. Math. Anal., 47 (2015), 3029-3115.  doi: 10.1137/140979708.

[39]

M. Winkler, Small-mass solution in the two-dimensionsl Keller-Segel system coupled to the Navier-Stokes equations, SIAM J. Math. Anal., 52 (2020), 2041-2080.  doi: 10.1137/19M1264199.

[40]

M. Winkler, $L^1$ solutions to parabolic Keller-Segel systems involving arbitrary superlinear degradation, preprint.

[41]

M. Winker, Global boundedness of solutions on the two-dimensional forager-exploiter model with logistic source, Discrete Contin. Dyn. Syst. Ser., 41 (2021), 3031-3043. 

[42]

T. Xiang, Chemotactic aggregation versus logistic damping on boundedness in the 3D minimal Keller-Segel Model, SIAM J. Appl. Math., 78 (2018), 2420-2438.  doi: 10.1137/17M1150475.

[43]

Q. Zhang and Y. Li, Global boundedness of solutions to a two-species chemotaxis system, Z. Angew. Math. Mech., 66 (2015), 83-93.  doi: 10.1007/s00033-013-0383-4.

[1]

Lu Xu, Chunlai Mu, Qiao Xin. Global boundedness of solutions to the two-dimensional forager-exploiter model with logistic source. Discrete and Continuous Dynamical Systems, 2021, 41 (7) : 3031-3043. doi: 10.3934/dcds.2020396
[2]

Ling Liu, Jiashan Zheng. Global existence and boundedness of solution of a parabolic-parabolic-ODE chemotaxis-haptotaxis model with (generalized) logistic source. Discrete and Continuous Dynamical Systems - B, 2019, 24 (7) : 3357-3377. doi: 10.3934/dcdsb.2018324
[3]

Sainan Wu, Junping Shi, Boying Wu. Global existence of solutions to an attraction-repulsion chemotaxis model with growth. Communications on Pure and Applied Analysis, 2017, 16 (3) : 1037-1058. doi: 10.3934/cpaa.2017050
[4]

Abelardo Duarte-Rodríguez, Lucas C. F. Ferreira, Élder J. Villamizar-Roa. Global existence for an attraction-repulsion chemotaxis fluid model with logistic source. Discrete and Continuous Dynamical Systems - B, 2019, 24 (2) : 423-447. doi: 10.3934/dcdsb.2018180
[5]

Feng Li, Yuxiang Li. Global existence of weak solution in a chemotaxis-fluid system with nonlinear diffusion and rotational flux. Discrete and Continuous Dynamical Systems - B, 2019, 24 (10) : 5409-5436. doi: 10.3934/dcdsb.2019064
[6]

Laiqing Meng, Jia Yuan, Xiaoxin Zheng. Global existence of almost energy solution to the two-dimensional chemotaxis-Navier-Stokes equations with partial diffusion. Discrete and Continuous Dynamical Systems, 2019, 39 (6) : 3413-3441. doi: 10.3934/dcds.2019141
[7]

Chunhua Jin. Global classical solution and stability to a coupled chemotaxis-fluid model with logistic source. Discrete and Continuous Dynamical Systems, 2018, 38 (7) : 3547-3566. doi: 10.3934/dcds.2018150
[8]

Xueli Bai, Wenji Zhang. Global generalized solutions to a chemotaxis model of capillary-sprout growth during tumor angiogenesis. Discrete and Continuous Dynamical Systems, 2021, 41 (9) : 4065-4083. doi: 10.3934/dcds.2021028
[9]

Qi Wang, Lu Zhang, Jingyue Yang, Jia Hu. Global existence and steady states of a two competing species Keller--Segel chemotaxis model. Kinetic and Related Models, 2015, 8 (4) : 777-807. doi: 10.3934/krm.2015.8.777
[10]

Changchun Liu, Pingping Li. Global existence for a chemotaxis-haptotaxis model with $ p $-Laplacian. Communications on Pure and Applied Analysis, 2020, 19 (3) : 1399-1419. doi: 10.3934/cpaa.2020070
[11]

Marco Di Francesco, Alexander Lorz, Peter A. Markowich. Chemotaxis-fluid coupled model for swimming bacteria with nonlinear diffusion: Global existence and asymptotic behavior. Discrete and Continuous Dynamical Systems, 2010, 28 (4) : 1437-1453. doi: 10.3934/dcds.2010.28.1437
[12]

Nikolaos Bournaveas, Vincent Calvez. Global existence for the kinetic chemotaxis model without pointwise memory effects, and including internal variables. Kinetic and Related Models, 2008, 1 (1) : 29-48. doi: 10.3934/krm.2008.1.29
[13]

Harumi Hattori, Aesha Lagha. Global existence and decay rates of the solutions for a chemotaxis system with Lotka-Volterra type model for chemoattractant and repellent. Discrete and Continuous Dynamical Systems, 2021, 41 (11) : 5141-5164. doi: 10.3934/dcds.2021071
[14]

T. Hillen, K. Painter, Christian Schmeiser. Global existence for chemotaxis with finite sampling radius. Discrete and Continuous Dynamical Systems - B, 2007, 7 (1) : 125-144. doi: 10.3934/dcdsb.2007.7.125
[15]

Tong Li, Anthony Suen. Existence of intermediate weak solution to the equations of multi-dimensional chemotaxis systems. Discrete and Continuous Dynamical Systems, 2016, 36 (2) : 861-875. doi: 10.3934/dcds.2016.36.861
[16]

Hua Zhong, Chunlai Mu, Ke Lin. Global weak solution and boundedness in a three-dimensional competing chemotaxis. Discrete and Continuous Dynamical Systems, 2018, 38 (8) : 3875-3898. doi: 10.3934/dcds.2018168
[17]

Zijuan Wen, Meng Fan, Asim M. Asiri, Ebraheem O. Alzahrani, Mohamed M. El-Dessoky, Yang Kuang. Global existence and uniqueness of classical solutions for a generalized quasilinear parabolic equation with application to a glioblastoma growth model. Mathematical Biosciences & Engineering, 2017, 14 (2) : 407-420. doi: 10.3934/mbe.2017025
[18]

Xin Lai, Xinfu Chen, Mingxin Wang, Cong Qin, Yajing Zhang. Existence, uniqueness, and stability of bubble solutions of a chemotaxis model. Discrete and Continuous Dynamical Systems, 2016, 36 (2) : 805-832. doi: 10.3934/dcds.2016.36.805
[19]

Dimitra Antonopoulou, Georgia Karali. Existence of solution for a generalized stochastic Cahn-Hilliard equation on convex domains. Discrete and Continuous Dynamical Systems - B, 2011, 16 (1) : 31-55. doi: 10.3934/dcdsb.2011.16.31
[20]

Huanhuan Qiu, Shangjiang Guo. Global existence and stability in a two-species chemotaxis system. Discrete and Continuous Dynamical Systems - B, 2019, 24 (4) : 1569-1587. doi: 10.3934/dcdsb.2018220

2021 Impact Factor: 1.497

Tools

Metrics

  • PDF downloads (347)
  • HTML views (255)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy