2015/07/07 by Fang Li, Li, Fang, Xing Liang +3
Mathematics · Medicine · #35B15 #35K20 #35K57 #37L30 #92B05 #Analysis of PDEs (math.AP) #Boundary (topology) #Boundary value problem #FOS: Mathematics #Free boundary problem #Geology #Mathematical analysis #Mathematical and Theoretical Epidemiology and Ecology Models #Mathematics #Nonlinear Differential Equations Analysis #Numerical methods for differential equations #Physics #Series (stratigraphy) #Traveling wave #math.AP #msc:35B15 #msc:35K20 #msc:35K57 #msc:37L30 #msc:92B05
paper · pdf · doi:10.48550/arxiv.1507.01886
published in arXiv (Cornell University) (Cornell University) · 38 pages
arxiv created 2015/07/07 · openalex publication_date 2015/07/07 · arxiv updated 2015/07/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In this series of papers, we investigate the spreading and vanishing dynamics of time almost periodic diffusive KPP equations with free boundaries. Such equations are used to characterize the spreading of a new species in time almost periodic environments with free boundaries representing the spreading fronts. In the first part of the series, we showed that a spreading-vanishing dichotomy occurs for such free boundary problems (see [16]). In this second part of the series, we investigate the spreading speeds of such free boundary problems in the case that the spreading occurs. We first prove the existence of a unique time almost periodic semi-wave solution associated to such a free boundary problem. Using the semi-wave solution, we then prove that the free boundary problem has a unique spreading speed.