2018/05/28 by Alejandro Gárriz, Gárriz, Alejandro · 2 citations
Computer Science · Mathematics · Medicine · #35B40 #35K55 #35K65 #76S05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models
paper · pdf · doi:10.48550/arxiv.1805.10955
openalex publication_date 2018/05/28 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
We consider reaction-diffusion equations of porous medium type, with\ndifferent kind of reaction terms, and nonnegative bounded initial data. For all\nthe reaction terms under consideration there are initial data for which the\nsolution converges to 1 uniformly in compact sets for large times. We will\ncharacterize for which reaction terms this happens for all nontrivial\nnonnegative initial data, and for which ones there are also solutions\nconverging uniformly to 0. Problems in this family have a unique (up to\ntranslations) travelling wave with a finite front and we will see how its speed\ngives the asymptotic velocity of all the solutions with compactly supported\ninitial data. We will also prove in the one-dimensional case that solutions\nwith bounded compactly supported initial data converging to 1 do so approaching\na translation of this unique traveling wave. We will prove a similar result for\nnon-compactly supported initial data in a certain class.\n