Sharp estimates for the spreading speeds of the Lotka-Volterra diffusion system with strong competition

Peng, Rui; Wu, Chang-Hong; Zhou, Maolin

doi:10.1016/j.anihpc.2020.07.006

Peng, Rui ¹ ; Wu, Chang-Hong ² ; Zhou, Maolin ³

¹ a School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, 221116, Jiangsu Province, People's Republic of China
² b Department of Applied Mathematics, National Chiao Tung University, Hsinchu 300, Taiwan, Republic of China
³ c Chern Institute of Mathematics and LPMC, Nankai University, Tianjin, 300071, People's Republic of China

Annales de l'I.H.P. Analyse non linéaire, mai – juin 2021, Tome 38 (2021) no. 3, pp. 507-547.

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Résumé

This paper is concerned with the classical two-species Lotka-Volterra diffusion system with strong competition. The sharp dynamical behavior of the solution is established in two different situations: either one species is an invasive one and the other is a native one or both are invasive species. Our results seem to be the first that provide a precise spreading speed and profile for such a strong competition system. Among other things, our analysis relies on the construction of new types of supersolution and subsolution, which are optimal in certain sense.

Reçu le : 2019-08-14
Révisé le : 2020-05-25
Accepté le : 2020-07-13

DOI : 10.1016/j.anihpc.2020.07.006

Classification : 35K57, 35K45, 92D25
Mots-clés : Lotka-Volterra diffusion system, Strong competition, Traveling waves, Long-time behavior, Spreading speed and profile

Affiliations des auteurs :

Peng, Rui ¹ ; Wu, Chang-Hong ² ; Zhou, Maolin ³

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     author = {Peng, Rui and Wu, Chang-Hong and Zhou, Maolin},
     title = {Sharp estimates for the spreading speeds of the {Lotka-Volterra} diffusion system with strong competition},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {507--547},
     publisher = {Elsevier},
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Peng, Rui; Wu, Chang-Hong; Zhou, Maolin. Sharp estimates for the spreading speeds of the Lotka-Volterra diffusion system with strong competition. Annales de l'I.H.P. Analyse non linéaire, mai – juin 2021, Tome 38 (2021) no. 3, pp. 507-547. doi : 10.1016/j.anihpc.2020.07.006. http://archive.numdam.org/articles/10.1016/j.anihpc.2020.07.006/

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