Semi-wave and spreading speed for the diffusive competition model with a free boundary
By Yihong Du, Mingxin Wang, Maolin Zhou. 2015
102 citations recorded by the source corpus.
We determine the asymptotic spreading speed of an invasive species, which invades the territory of a native competitor, governed by a diffusive competition model with a free boundary in a spherically symmetric setting. This free boundary problem was studied recently in [7] but only rough bounds of the spreading speed was obtained there. We show in this paper that the spreading speed has an asymptotic limit (as time goes to infnity), which is given by a certain traveling wave type system of one space dimension, called a semi-wave. This appears to be the first result that gives the precise asymptotic spreading speed for a two species system with free boundaries.
Subfields: Genetics, Mathematical Physics, Public Health, Environmental and Occupational Health
View Paper: https://www.semanticscholar.org/paper/3d96fbcfcf13fb6a49aca80e59b948d731fb749f
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Citations in the corpus
- Invasion of open space by two competitors: spreading properties of monostable two‐species competition‐diffusion systems (2018, background): “Y. Du, M. Wang and M. Zhou, ‘Semi-wave and spreading speed for the diffusive competition model with a free boundary’, J. Math.”
- Two species nonlocal diffusion systems with free boundaries (2019, background): “In the case of local diffusion, competition and prey-predator models with free boundaries appearing in only one species were considered in [10, 12, 38], and with independent free boundaries for the two species were studied in [13, 15, 33, 34].”
- Dynamics for a diffusive prey-predator model with different free boundaries (2015, background): “The authors of [10, 15, 32, 33, 47] investigated a competition model in which the invasive species exists initially in a ball and invades into the new environment,”
- The dynamics of a Fisher-KPP nonlocal diffusion model with free boundaries (2018, background): “Among the many further extensions, we only mention the extension to various heterogeneous environments in [12, 13, 15, 16, 30, 31, 40], and extensions to certain Lotka-Volterra two-species systems and epidemic models in [18,21,24,39] and [7, 23,33] (see also the references therein).”