# 【研究成果】 物種間的權衡與競爭：探究自然界物種的擴張現象

680 觀看次數

$$u\left(0,x\right)=u_0\left(x\right),\ \ v\left(0,x\right)=v_0\left(x\right),\ \ x\in\mathbb{R},$$

### 參考文獻

[1]  Y. Du, Z.G. Lin, Spreading-vanishing dichotomy in the diffusive logistic model with a free boundary, SIAM J. Math. Anal., 42 (2010), 377–405.

[2] Y. Du, C.-H. Wu, Spreading with two speeds and mass segregation in a diffusive competition system with free boundaries, Cal. Var. PDE (2018) 57:52.

[3]  Y. Du, C.-H. Wu, Classification of the spreading behaviors of a two-species diffusioncompetition system with free boundaries, Cal. Var. PDE, (2022) 61: 54.

[4]  R. A. Fisher, The wave of advance of advantageous genes, Ann. Eugen., 7 (1937), 335-369.

[5] J.-S. Guo, C.-H. Wu, Entire solutions originating from traveling fronts for a two-species competition-diffusion system, Nonlinearity, 32 (2019) 3234.

[6] H. Izuhara, H. Monobe, C.-H. Wu, The formation of spreading front: the singular limit of three-component reaction-diffusion models, J. Math. Biol. 82 38 (2021).

[7] K. Khan, S. Liu, T.M. Schaerf, Y. Du, Invasive behaviour under competition via a free boundary model: a numerical approach. J. Math. Biol. 83, 23 (2021).

[8] A. N. Kolmogorov, I. G. Petrovskii and N. S. Piskunov, A study of the equation of diffusion with increase in the quantity of matter, and its application to a biological problem, Bull. Moscow State Univ. Ser. A: Math. and Mech., 1 (1937), 1-25.

[9] Y. Lou, Some challenging mathematical problems in evolution of dispersal and population dynamics, in Tutorials in Mathematical Biosciences. IV, Lecture Notes in Math. 1922, Springer, Berlin, 2008, 171—205.

[10] M. Mimura, Y. Yamada, S. Yotsutani, A free boundary problem in ecology, Japan J. Appl. Math. 2 (1985), 151–186.

[11] R. Peng, C.-H. Wu, and M. Zhou, Sharp estimates for the spreading speed of the Lotka-Volterra diffusion system with strong competition, Annales de l’Institut Henri Poincare (C) Non Linear Analysis, 38 (2021) 507-547.

[12] N. Shigesada, K. Kawasaki, Biological Invasions: Theory and Practice, Oxford Series in Ecology and Evolution, Oxford: Oxford UP, 1997.

[13] C.-H. Wu, Biased movement and the ideal free distribution in some free boundary problems, J. Diff. Eqns 265 (2018), 4251–4282

0 迴響