Heterogeneous Diffusion and Nonlinear Advection in a One-Dimensional Fisher-KPP Problem

The goal of this study is to provide an analysis of a Fisher-KPP non-linear reaction problem with a higher-order diffusion and a non-linear advection. We study the existence and uniqueness of solutions together with asymptotic solutions and positivity conditions. We show the existence of instabiliti...

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Published inEntropy (Basel, Switzerland) Vol. 24; no. 7; p. 915
Main Authors Palencia, José Luis Díaz, Rahman, Saeed ur, Redondo, Antonio Naranjo
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 30.06.2022
MDPI
Subjects
Advection
asymptotic
Asymptotic methods
Diffusion
Evolution
existence
Fisher-KPP problem
Hamilton-Jacobi equation
higher-order diffusion
instabilities
Uniqueness
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ISSN1099-4300
1099-4300
DOI10.3390/e24070915

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Summary:The goal of this study is to provide an analysis of a Fisher-KPP non-linear reaction problem with a higher-order diffusion and a non-linear advection. We study the existence and uniqueness of solutions together with asymptotic solutions and positivity conditions. We show the existence of instabilities based on a shooting method approach. Afterwards, we study the existence and uniqueness of solutions as an abstract evolution of a bounded continuous single parametric (t) semigroup. Asymptotic solutions based on a Hamilton–Jacobi equation are then analyzed. Finally, the conditions required to ensure a comparison principle are explored supported by the existence of a positive maximal kernel.
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ISSN:1099-4300
1099-4300
DOI:10.3390/e24070915