Semigroup theory and asymptotic profiles of solutions for a higher-order Fisher-KPP problem in R^N
| dc.contributor.author | Diaz Palencia, Jose Luis | |
| dc.date.accessioned | 2023-05-19T19:20:58Z | |
| dc.date.available | 2023-05-19T19:20:58Z | |
| dc.date.issued | 2023-01-16 | |
| dc.description.abstract | We study a reaction-diffusion problem formulated with a higher-order operator, a non-linear advection, and a Fisher-KPP reaction term depending on the spatial variable. The higher-order operator induces solutions to oscillate in the proximity of an equilibrium condition. Given this oscillatory character, solutions are studied in a set of bounded domains. We introduce a new extension operator, that allows us to study the solutions in the open domain RN, but departing from a sequence of bounded domains. The analysis about regularity of solutions is built based on semigroup theory. In this approach, the solutions are interpreted as an abstract evolution given by a bounded continuous operator. Afterward, asymptotic profiles of solutions are studied based on a Hamilton-Jacobi equation that is obtained with a single point exponential scaling. Finally, a numerical assessment, with the function bvp4c in Matlab, is introduced to discuss on the validity of the hypothesis. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 17 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Díaz Palencia, J. L. (2023). Semigroup theory and asymptotic profiles of solutions for a higher-order Fisher-KPP problem in R^N. Electronic Journal of Differential Equations, 2023(04), pp. 1-17. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/16839 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2022, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Higher order diffusion | |
| dc.subject | Semigroup theory | |
| dc.subject | Fisher-KPP equation | |
| dc.subject | Hamilton-Jacobi equation | |
| dc.title | Semigroup theory and asymptotic profiles of solutions for a higher-order Fisher-KPP problem in R^N | en_US |
| dc.type | Article |