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Shi, Linfei; Xu, Tianzhou; Mao, Jinjin

Dynamics of a mutualistic model with advection and a free boundary in heterogeneous environment. (English) Zbl 1523.35307

J. Appl. Math. Comput. 69, No. 4, 3261-3288 (2023).

Cited in 1 Document

MSC:

35R35 Free boundary problems for PDEs
35B40 Asymptotic behavior of solutions to PDEs
35K51 Initial-boundary value problems for second-order parabolic systems
35K57 Reaction-diffusion equations
92D25 Population dynamics (general)

Keywords:

mutualistic model; free boundary; heterogeneous environment; spreading and vanishing
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Full Text: DOI

References:

[1] Du, Y.; Lin, Z., Spreading-vanishing dichotomy in the diffusive logistic model with a free boundary, SIAM J. Math. Anal., 42, 377-405 (2010) · Zbl 1219.35373 · doi:10.1137/090771089
[2] Bunting, G.; Du, Y.; Krakowski, K., Spreading speed revisited: analysis of a free boundary model, Netw. Heterog. Media., 7, 4, 583-603 (2012) · Zbl 1302.35194 · doi:10.3934/nhm.2012.7.583
[3] Kaneko, Y.; Yamada, Y., A free boundary problem for a reaction-diffusion equation appearing in ecology, Adv. Math. Sci. Appl., 21, 2, 467-492 (2011) · Zbl 1254.35248
[4] Peng, R.; Zhao, X., The diffusive logistic model with a free boundary and seasonal succession, Discrete Contin. Dyn. Syst., 33, 5, 2007-2031 (2013) · Zbl 1273.35327 · doi:10.3934/dcds.2013.33.2007
[5] Du, Y.; Lou, B., Spreading and vanishing in nonlinear diffusion problems with free boundaries, J. Eur. Math. Soc., 17, 10, 2673-2724 (2015) · Zbl 1331.35399 · doi:10.4171/JEMS/568
[6] Maidana, N.; Yang, H., Spatial spreading of West Nile Virus described by traveling waves, J. Theoret. Biol., 258, 403-417 (2009) · Zbl 1405.92260 · doi:10.1016/j.jtbi.2008.12.032
[7] Averill, I., The Effect of Intermediate Advection on Two Competing Species (2012), Doctor of Philosophy: Ohio State University, Mathematics, Doctor of Philosophy
[8] Gu, H.; Lin, Z.; Lou, B., Long time behavior of solutions of a diffusion-advection logistic model with free boundaries, Appl. Math. Lett., 37, 49-53 (2014) · Zbl 1320.35069 · doi:10.1016/j.aml.2014.05.015
[9] Gu, H.; Lou, B.; Zhou, M., Long time behavior of solutions of Fisher-KPP equation with advection and free boundaries, J. Funct. Anal., 269, 6, 1714-1768 (2015) · Zbl 1335.35102 · doi:10.1016/j.jfa.2015.07.002
[10] Kaneko, Y.; Matsuzawa, H., Spreading speed and sharp asymptotic profiles of solutions in free boundary problems for nonlinear advection-diffusion equations, J. Math. Anal. Appl., 428, 1, 43-76 (2015) · Zbl 1325.35292 · doi:10.1016/j.jmaa.2015.02.051
[11] Gu, H.; Lou, B., Spreading in advective environment modeled by a reaction diffusion equation with free boundaries, J. Differ. Eqn., 260, 3991-4015 (2016) · Zbl 1335.35119 · doi:10.1016/j.jde.2015.11.002
[12] Zhou, P.; Xiao, D., Global dynamics of a classical Lotka-Volterra competition-diffusion-advection system, J. Funct. Anal., 275, 2, 356-380 (2018) · Zbl 1390.35166 · doi:10.1016/j.jfa.2018.03.006
[13] Zhao, Y.; Wang, M., A reaction-diffusion-advection equation with mixed and free boundary conditions, J. Dyn. Differ. Eqn., 30, 2, 743-777 (2018) · Zbl 1395.35106 · doi:10.1007/s10884-017-9571-9
[14] Li, M.; Lin, Z., The spreading fronts in a mutualistic model with advection, Discrete Contin. Dyn. Syst. Ser. B, 20, 7, 2089-2105 (2015) · Zbl 1334.35441 · doi:10.3934/dcdsb.2015.20.2089
[15] Zhao, Y.; Wang, M., Free boundary problems for the diffusive competition system in higher dimension with sign-changing coefficients, IMA J. Appl. Math., 81, 2, 255-280 (2016) · Zbl 1338.35444 · doi:10.1093/imamat/hxv035
[16] Du, Y.; Guo, Z., Spreading-vanishing dichotomy in a diffusive logistic model with a free boundary, II, J. Differ. Eqn., 250, 4336-4366 (2011) · Zbl 1222.35096 · doi:10.1016/j.jde.2011.02.011
[17] Du Y., Liang X.: Pulsating semi-waves in periodic media and spreading speed determined by a free boundary model. Ann. Inst. H. Poincaré Anal. Non linéaire 32(2), 279-305 (2015). doi:10.1016/j.anihpc.2013.11.004 · Zbl 1321.35263
[18] Ding, W.; Peng, R.; Wei, L., The diffusive logistic model with a free boundary in a heterogeneous time-periodic environment, J. Differ. Eqn., 263, 5, 2736-2779 (2017) · Zbl 1515.35361 · doi:10.1016/j.jde.2017.04.013
[19] Du, Y.; Guo, Z.; Peng, R., A diffusive logistic model with a free boundary in time-periodic environment, J. Funct. Anal., 265, 9, 2089-2142 (2013) · Zbl 1282.35419 · doi:10.1016/j.jfa.2013.07.016
[20] Wang, M., A diffusive logistic equation with a free boundary and sign-changing coefficient in time-periodic environment, J. Funct. Anal., 270, 2, 483-508 (2016) · Zbl 1335.35128 · doi:10.1016/j.jfa.2015.10.014
[21] Zhou, P.; Xiao, D., The diffusive logistic model with a free boundary in heterogeneous environment, J. Differ. Eqn., 256, 6, 927-1954 (2014) · Zbl 1316.35156 · doi:10.1016/j.jde.2013.12.008
[22] Wang, J.; Zhang, L., Invasion by an inferior or superior competitor: a diffusive competition model with a free boundary in a heterogeneous environment, J. Math. Anal. Appl., 423, 1, 377-398 (2015) · Zbl 1315.35219 · doi:10.1016/j.jmaa.2014.09.055
[23] Zhao, J.; Wang, M., A free boundary problem of a predator-prey model with higher dimension and heterogeneous environment, Nonlinear Anal. Real World Appl., 16, 250-263 (2014) · Zbl 1296.35220 · doi:10.1016/j.nonrwa.2013.10.003
[24] Wang, M., Existence and uniqueness of solutions of free boundary problems in heterogeneous environments, Discrete Contin. Dyn. Syst. Ser. B, 24, 2, 415-421 (2019) · Zbl 1404.35230 · doi:10.3934/dcdsb.2018179
[25] Monobe, H.; Wu, C., On a free boundary problem for a reaction-diffusion-advection logistic model in heterogeneous environment, J. Differ. Eqn., 261, 6144-6177 (2016) · Zbl 1351.35070 · doi:10.1016/j.jde.2016.08.033
[26] Tang, D.; Zhou, P., On a Lotka-Volterra competition-diffusion-advection System: homogeneity vs heterogeneity, J. Differ. Eqn., 268, 4, 1570-1599 (2020) · Zbl 1427.35129 · doi:10.1016/j.jde.2019.09.003
[27] Chen, Q.; Li, F.; Wang, F., A reaction-diffusion-advection competition model with two free boundaries in heterogeneous time-periodic environment, IMA J. Appl. Math., 82, 2, 445-470 (2017) · Zbl 1404.92146 · doi:10.1093/imamat/hxw059
[28] Duan, B.; Zhang, Z., A reaction-diffusion-advection two-species competition system with a free boundary in heterogeneous environment, Discrete Contin. Dyn. Syst. Ser. B, 27, 837-861 (2022) · Zbl 1481.35409 · doi:10.3934/DCDSB.2021067
[29] May, M., Simple mathematical models with very complicated dynamics, Nature, 261, 459-467 (1976) · Zbl 1369.37088 · doi:10.1038/261459a0
[30] Zhang, Q.; Wang, M., Dynamics for the diffusive mutualist model with advection and different free boundaries, J. Math. Anal. Appl., 472, 1512-1535 (2019) · Zbl 1416.35286 · doi:10.1016/j.jmaa.2019.02.037
[31] Wang, M., The diffusive logistic equation with a free boundary and sign-changing coefficient, J. Differ. Eqn., 258, 4, 1252-1266 (2015) · Zbl 1319.35094 · doi:10.1016/j.jde.2014.10.022
[32] Du, Y.; Guo, Z., The Stefan problem for the Fisher-KPP equation, J. Differ. Eqn., 253, 3, 996-1035 (2012) · Zbl 1257.35110 · doi:10.1016/j.jde.2012.04.014
[33] Wang, M.; Zhao, J., A free boundary problem for the predator-prey model with double free boundaries, J. Dyn. Differ. Eqn., 29, 3, 957-979 (2017) · Zbl 1373.35164 · doi:10.1007/s10884-015-9503-5
[34] Wang, M., On some free boundary problems of the prey-predator model, J. Differ. Eqn., 256, 10, 3365-3394 (2014) · Zbl 1317.35110 · doi:10.1016/j.jde.2014.02.013
[35] Gu, H.; Lin, Z.; Lou, B., Different asymptotic spreading speeds induced by advection in a diffusion problem with free boundaries, Proc. Am. Math. Soc., 143, 3, 1109-1117 (2015) · Zbl 1310.35062 · doi:10.1090/S0002-9939-2014-12214-3
[36] Cantrell, R.; Cosner, C.; Lou, Y., Movement toward better environments and the evolution of rapid diffusion, Math. Biosci., 204, 2, 199-214 (2006) · Zbl 1105.92036 · doi:10.1016/j.mbs.2006.09.003
[37] Lam, K.; Liu, S.; Lou, Y., Selected topics on reaction-diffusion-advection models from spatial ecology, Math. Appl. Sci. Eng., 1, 91-206 (2020) · Zbl 1498.92304 · doi:10.5206/mase/10644
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