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Global classical solutions to a kind of mixed initialboundary value problem for quasilinear hyperbolic systems
Two species competition with an inhibitor involved
1.  Department of Mathematics, Auburn University, AL 368495310, United States, United States 
[1] 
Suqing Lin, Zhengyi Lu. Permanence for twospecies LotkaVolterra systems with delays. Mathematical Biosciences & Engineering, 2006, 3 (1) : 137144. doi: 10.3934/mbe.2006.3.137 
[2] 
Guichen Lu, Zhengyi Lu. Permanence for twospecies LotkaVolterra cooperative systems with delays. Mathematical Biosciences & Engineering, 2008, 5 (3) : 477484. doi: 10.3934/mbe.2008.5.477 
[3] 
GuoBao Zhang, Ruyun Ma, XueShi Li. Traveling waves of a LotkaVolterra strong competition system with nonlocal dispersal. Discrete & Continuous Dynamical Systems  B, 2018, 23 (2) : 587608. doi: 10.3934/dcdsb.2018035 
[4] 
Jifa Jiang, Fensidi Tang. The complete classification on a model of two species competition with an inhibitor. Discrete & Continuous Dynamical Systems  A, 2008, 20 (3) : 659672. doi: 10.3934/dcds.2008.20.659 
[5] 
William Clark, Anthony Bloch, Leonardo Colombo. A PoincaréBendixson theorem for hybrid systems. Mathematical Control & Related Fields, 2019, 0 (0) : 00. doi: 10.3934/mcrf.2019028 
[6] 
ChiunChuan Chen, YinLiang Huang, LiChang Hung, ChangHong Wu. Semiexact solutions and pulsating fronts for LotkaVolterra systems of two competing species in spatially periodic habitats. Communications on Pure & Applied Analysis, 2020, 19 (1) : 118. doi: 10.3934/cpaa.2020001 
[7] 
HaiYang Jin, Tian Xiang. Convergence rates of solutions for a twospecies chemotaxisNavierStokes sytstem with competitive kinetics. Discrete & Continuous Dynamical Systems  B, 2019, 24 (4) : 19191942. doi: 10.3934/dcdsb.2018249 
[8] 
TingHui Yang, Weinian Zhang, Kaijen Cheng. Global dynamics of three species omnivory models with LotkaVolterra interaction. Discrete & Continuous Dynamical Systems  B, 2016, 21 (8) : 28672881. doi: 10.3934/dcdsb.2016077 
[9] 
LihIng W. Roeger, Razvan Gelca. Dynamically consistent discretetime LotkaVolterra competition models. Conference Publications, 2009, 2009 (Special) : 650658. doi: 10.3934/proc.2009.2009.650 
[10] 
Yuan Lou, Dongmei Xiao, Peng Zhou. Qualitative analysis for a LotkaVolterra competition system in advective homogeneous environment. Discrete & Continuous Dynamical Systems  A, 2016, 36 (2) : 953969. doi: 10.3934/dcds.2016.36.953 
[11] 
Yukio KanOn. Global bifurcation structure of stationary solutions for a LotkaVolterra competition model. Discrete & Continuous Dynamical Systems  A, 2002, 8 (1) : 147162. doi: 10.3934/dcds.2002.8.147 
[12] 
Jian Fang, Jianhong Wu. Monotone traveling waves for delayed LotkaVolterra competition systems. Discrete & Continuous Dynamical Systems  A, 2012, 32 (9) : 30433058. doi: 10.3934/dcds.2012.32.3043 
[13] 
JongShenq Guo, YingChih Lin. The sign of the wave speed for the LotkaVolterra competitiondiffusion system. Communications on Pure & Applied Analysis, 2013, 12 (5) : 20832090. doi: 10.3934/cpaa.2013.12.2083 
[14] 
Qi Wang, Chunyi Gai, Jingda Yan. Qualitative analysis of a LotkaVolterra competition system with advection. Discrete & Continuous Dynamical Systems  A, 2015, 35 (3) : 12391284. doi: 10.3934/dcds.2015.35.1239 
[15] 
Qi Wang, Yang Song, Lingjie Shao. Boundedness and persistence of populations in advective LotkaVolterra competition system. Discrete & Continuous Dynamical Systems  B, 2018, 23 (6) : 22452263. doi: 10.3934/dcdsb.2018195 
[16] 
KuangHui Lin, Yuan Lou, ChihWen Shih, TzeHung Tsai. Global dynamics for twospecies competition in patchy environment. Mathematical Biosciences & Engineering, 2014, 11 (4) : 947970. doi: 10.3934/mbe.2014.11.947 
[17] 
S.A. Gourley, Yang Kuang. TwoSpecies Competition with High Dispersal: The Winning Strategy. Mathematical Biosciences & Engineering, 2005, 2 (2) : 345362. doi: 10.3934/mbe.2005.2.345 
[18] 
Linping Peng, Zhaosheng Feng, Changjian Liu. Quadratic perturbations of a quadratic reversible LotkaVolterra system with two centers. Discrete & Continuous Dynamical Systems  A, 2014, 34 (11) : 48074826. doi: 10.3934/dcds.2014.34.4807 
[19] 
Hélène Leman, Sylvie Méléard, Sepideh Mirrahimi. Influence of a spatial structure on the long time behavior of a competitive LotkaVolterra type system. Discrete & Continuous Dynamical Systems  B, 2015, 20 (2) : 469493. doi: 10.3934/dcdsb.2015.20.469 
[20] 
Yubin Liu, Peixuan Weng. Asymptotic spreading of a three dimensional LotkaVolterra cooperativecompetitive system. Discrete & Continuous Dynamical Systems  B, 2015, 20 (2) : 505518. doi: 10.3934/dcdsb.2015.20.505 
2018 Impact Factor: 1.143
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