×

Asymptotic spreading of a diffusive competition model with different free boundaries. (English) Zbl 1412.35166

As a follow-up work of M. Wang and Y. Zhang [J. Differ. Equations 264, No. 5, 3527–3558 (2018; Zbl 1391.35191)], this paper investigates a free boundary problem of a diffusive competition model with two different free boundaries. Estimates of asymptotic spreading speeds of two species and asymptotic speeds of two free boundaries are obtained.

MSC:

35K51 Initial-boundary value problems for second-order parabolic systems
35R35 Free boundary problems for PDEs
92B05 General biology and biomathematics

Citations:

Zbl 1391.35191
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Du, Y. H.; Guo, Z. M., Spreading-vanishing dichotomy in a diffusive logistic model with a free boundary, II, J. Differential Equations, 250, 12, 4336-4366 (2011) · Zbl 1222.35096
[2] Du, Y. H.; Lin, Z. G., Spreading-vanishing dichotomy in a diffusive logistic model with a free boundary, SIAM J. Math. Anal.. SIAM J. Math. Anal., SIAM J. Math. Anal., 45, 3, 1995-1996 (2013), Erratum: · Zbl 1275.35156
[3] Du, Y. H.; Lin, Z. G., The diffusive competition model with a free boundary: invasion of a superior or inferior competitor, Discrete Contin. Dyn. Syst. Ser. B, 19, 10, 3105-3132 (2014) · Zbl 1310.35245
[4] Du, Y. H.; Lou, B. D., Spreading and vanishing in nonlinear diffusion problems with free boundaries, J. Eur. Math. Soc., 17, 10, 2673-2724 (2015) · Zbl 1331.35399
[5] Du, Y. H.; Matsuzawa, H.; Zhou, M. L., Sharp estimate of the spreading speed determined by nonlinear free boundary problems, SIAM J. Math. Anal., 46, 1, 375-396 (2014) · Zbl 1296.35219
[6] Du, Y. H.; Wang, M. X.; Zhou, M. L., Semi-wave and spreading speed for the diffusive competition model with a free boundary, J. Math. Pures Appl., 107, 3, 253-287 (2017) · Zbl 1377.35136
[7] Du, Y. H.; Wu, C-H., Spreading with two speeds and mass segregation in a diffusive competition system with free boundaries, Calc. Var. Partial Differential Equations, 57, 2, Article 52 pp. (2018) · Zbl 1396.35028
[8] Fife, P. C.; Mxleod, J. B., The approach of solutions of nonlinear diffusion equation to travelling front solutions, Arch. Ration. Mech. Anal., 65, 4, 335-361 (1977) · Zbl 0361.35035
[9] Gu, H.; Lou, B. D.; Zhou, M. L., Long time behavior for solutions of Fisher-KPP equation with advection and free boundaries, J. Funct. Anal., 269, 1714-1768 (2015) · Zbl 1335.35102
[10] Guo, J. S.; Wu, C. H., On a free boundary problem for a two-species weak competition system, J. Dynam. Differential Equations, 24, 4, 873-895 (2012) · Zbl 1263.35132
[11] Guo, J. S.; Wu, C. H., Dynamics for a two-species competition-diffusion model with two free boundaries, Nonlinearity, 28, 1, 1-27 (2015) · Zbl 1316.92066
[12] Krakowski, K.; Du, Y. H.; Bunting, G., Spreading speed revisited: analysis of a free boundary mode, Netw. Heterog. Media, 7, 4, 583-603 (2012) · Zbl 1302.35194
[13] 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
[14] Lin, G.; Li, W. T., Asymptotic spreading of competition diffusion systems: the role of interspecific competitions, European J. Appl. Math., 23, 669-689 (2012) · Zbl 1256.35179
[15] Wu, C. H., The minimal habitat size for spreading in a weak competition system with two free boundaries, J. Differential Equations, 259, 3, 873-897 (2015) · Zbl 1319.35081
[16] 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
[17] Wang, M. X., On some free boundary problems of the prey-predator model, J. Differential Equations, 256, 10, 3365-3394 (2014) · Zbl 1317.35110
[18] Wang, M. X., Spreading and vanishing in the diffusive prey-predator model with a free boundary, Commun. Nonlinear Sci. Numer. Simul., 23, 1-3, 311-327 (2015) · Zbl 1354.92074
[19] Wang, M. X.; Zhang, Q. Y., Dynamics for the diffusive Leslie-Gower model with double free boundaries, Discrete Contin. Dyn. Syst. A, 38, 5, 2591-2607 (2018) · Zbl 1393.35086
[20] Wang, M. X.; Zhang, Y., The time-periodic diffusive competition models with a free boundary and sign-changing growth rates, Z. Angew. Math. Phys., 67, 5, 132 (2016) · Zbl 1359.35093
[21] Wang, M. X.; Zhang, Y., Note on a two-species competition-diffusion model with two free boundaries, Nonlinear Anal. TMA, 159, 458-467 (2017) · Zbl 1371.35367
[22] Wang, M. X.; Zhang, Y., Dynamics for a diffusive prey-predator model with different free boundaries, J. Differential Equations, 264, 3527-3558 (2018) · Zbl 1391.35191
[23] Wang, M. X.; Zhao, J. F., Free boundary problems for a Lotka-Volterra competition system, J. Dynam. Differential Equations, 26, 3, 655-672 (2014) · Zbl 1304.35783
[24] Wang, M. X.; Zhao, J. F., A free boundary problem for a predator-prey model with double free boundaries, J. Dynam. Differential Equations, 29, 3, 957-979 (2017) · Zbl 1373.35164
[25] Zhao, J. F.; Wang, M. X., 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
[26] Zhao, Y. G.; Wang, M. X., 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
[27] Zhao, Y. G.; Wang, M. X., A reaction-diffusion-advection equation with mixed and free boundaries, J. Dynam. Differential Equations, 30, 2, 743-777 (2018) · Zbl 1395.35106
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.