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Global existence and internal stabilization for a reaction-diffusion system posed on non coincident spatial domains
1. | Faculty of Mathematics, University “Al.I. Cuza” and, Institute of Mathematics “Octav Mayer”, Iaşi 700506 |
2. | Departments of Engineering Technology and Mathematics, University of Houston, Houston, Texas 77204-3476, United States |
3. | Université Victor Segalen Bordeaux 2, case 26, UMR CNRS 5251 IMB & INRIA Futurs Anubis, 146, rue Léo Saignat, 33076 Bordeaux Cedex |
[1] |
Arnaud Ducrot, Vincent Guyonne, Michel Langlais. Some remarks on the qualitative properties of solutions to a predator-prey model posed on non coincident spatial domains. Discrete and Continuous Dynamical Systems - S, 2011, 4 (1) : 67-82. doi: 10.3934/dcdss.2011.4.67 |
[2] |
Jiang Liu, Xiaohui Shang, Zengji Du. Traveling wave solutions of a reaction-diffusion predator-prey model. Discrete and Continuous Dynamical Systems - S, 2017, 10 (5) : 1063-1078. doi: 10.3934/dcdss.2017057 |
[3] |
Mostafa Bendahmane. Analysis of a reaction-diffusion system modeling predator-prey with prey-taxis. Networks and Heterogeneous Media, 2008, 3 (4) : 863-879. doi: 10.3934/nhm.2008.3.863 |
[4] |
Wenshu Zhou, Hongxing Zhao, Xiaodan Wei, Guokai Xu. Existence of positive steady states for a predator-prey model with diffusion. Communications on Pure and Applied Analysis, 2013, 12 (5) : 2189-2201. doi: 10.3934/cpaa.2013.12.2189 |
[5] |
Guoqiang Ren, Bin Liu. Global existence and convergence to steady states for a predator-prey model with both predator- and prey-taxis. Discrete and Continuous Dynamical Systems, 2022, 42 (2) : 759-779. doi: 10.3934/dcds.2021136 |
[6] |
Sebastién Gaucel, Michel Langlais. Some remarks on a singular reaction-diffusion system arising in predator-prey modeling. Discrete and Continuous Dynamical Systems - B, 2007, 8 (1) : 61-72. doi: 10.3934/dcdsb.2007.8.61 |
[7] |
Liang Zhang, Zhi-Cheng Wang. Spatial dynamics of a diffusive predator-prey model with stage structure. Discrete and Continuous Dynamical Systems - B, 2015, 20 (6) : 1831-1853. doi: 10.3934/dcdsb.2015.20.1831 |
[8] |
Yang Lu, Xia Wang, Shengqiang Liu. A non-autonomous predator-prey model with infected prey. Discrete and Continuous Dynamical Systems - B, 2018, 23 (9) : 3817-3836. doi: 10.3934/dcdsb.2018082 |
[9] |
Andrei Korobeinikov. Global properties of a general predator-prey model with non-symmetric attack and consumption rate. Discrete and Continuous Dynamical Systems - B, 2010, 14 (3) : 1095-1103. doi: 10.3934/dcdsb.2010.14.1095 |
[10] |
Xiaoyan Zhang, Yuxiang Zhang. Spatial dynamics of a reaction-diffusion cholera model with spatial heterogeneity. Discrete and Continuous Dynamical Systems - B, 2018, 23 (6) : 2625-2640. doi: 10.3934/dcdsb.2018124 |
[11] |
Ting-Hao Hsu, Gail S. K. Wolkowicz. A criterion for the existence of relaxation oscillations with applications to predator-prey systems and an epidemic model. Discrete and Continuous Dynamical Systems - B, 2020, 25 (4) : 1257-1277. doi: 10.3934/dcdsb.2019219 |
[12] |
Angelo Favini, Atsushi Yagi. Global existence for Laplace reaction-diffusion equations. Discrete and Continuous Dynamical Systems - S, 2020, 13 (5) : 1473-1493. doi: 10.3934/dcdss.2020083 |
[13] |
H. W. Broer, K. Saleh, V. Naudot, R. Roussarie. Dynamics of a predator-prey model with non-monotonic response function. Discrete and Continuous Dynamical Systems, 2007, 18 (2&3) : 221-251. doi: 10.3934/dcds.2007.18.221 |
[14] |
Aniello Buonocore, Luigia Caputo, Enrica Pirozzi, Amelia G. Nobile. A non-autonomous stochastic predator-prey model. Mathematical Biosciences & Engineering, 2014, 11 (2) : 167-188. doi: 10.3934/mbe.2014.11.167 |
[15] |
Yinshu Wu, Wenzhang Huang. Global stability of the predator-prey model with a sigmoid functional response. Discrete and Continuous Dynamical Systems - B, 2020, 25 (3) : 1159-1167. doi: 10.3934/dcdsb.2019214 |
[16] |
Siqing Li, Zhonghua Qiao. A meshless collocation method with a global refinement strategy for reaction-diffusion systems on evolving domains. Discrete and Continuous Dynamical Systems - B, 2022, 27 (1) : 601-617. doi: 10.3934/dcdsb.2021057 |
[17] |
Walid Abid, Radouane Yafia, M.A. Aziz-Alaoui, Habib Bouhafa, Azgal Abichou. Global dynamics on a circular domain of a diffusion predator-prey model with modified Leslie-Gower and Beddington-DeAngelis functional type. Evolution Equations and Control Theory, 2015, 4 (2) : 115-129. doi: 10.3934/eect.2015.4.115 |
[18] |
Alexey Cheskidov, Songsong Lu. The existence and the structure of uniform global attractors for nonautonomous Reaction-Diffusion systems without uniqueness. Discrete and Continuous Dynamical Systems - S, 2009, 2 (1) : 55-66. doi: 10.3934/dcdss.2009.2.55 |
[19] |
Baifeng Zhang, Guohong Zhang, Xiaoli Wang. Threshold dynamics of a reaction-diffusion-advection Leslie-Gower predator-prey system. Discrete and Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021260 |
[20] |
Wei Wang, Wanbiao Ma. Global dynamics and travelling wave solutions for a class of non-cooperative reaction-diffusion systems with nonlocal infections. Discrete and Continuous Dynamical Systems - B, 2018, 23 (8) : 3213-3235. doi: 10.3934/dcdsb.2018242 |
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