A class of singular first order differential equations with applications in reaction-diffusion
type: Item
instance of: scholarly article
title: A class of singular first order differential equations with applications in reaction-diffusion
zbMATH Open document ID: 1269.34032
author: Andrea Gavioli
author: Ricardo Roque Enguiça
author: Luis Sanchez
published in: Discrete and Continuous Dynamical Systems
publication date: 2013-03-19T00:00:00Z
review text: The authors investigate the following first-order differential equation \[ y'=q(cy^{1/p}-f(u)), \] where \(c\) is a positive parameter, \(p, q\) greater than unity, are conjugate numbers and \(f\) is a continuous function such that \(f(0)=f(1)=0\). Solutions satisfying \(y(0)=y(1)=0\) are of particular interest from the physical point of view. Indeed, the equation stems from the Fisher reaction-diffusion equation when one looks for traveling wave solutions. According to the nonlinearity, three cases are discussed separately, including the stable and the bi-stable cases. Existence of positive solutions is then investigated together with their behavior near the origin and \(1\); the discussion takes into account the admissible values of the speed parameter \(c\) and the behavior of the ratio \(f(u)/u^{q-1}\) in the vicinity of the origin or on the interval \((0,1]\). The authors use shooting techniques.
reviewed by: Smail Djebali
Mathematics Subject Classification ID: 34B40
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 35K57
zbMATH DE Number: 6146681
zbMATH Keywords: \(p\)-Laplacian
zbMATH Keywords: FKPP equation
zbMATH Keywords: heteroclinic
zbMATH Keywords: travelling wave
zbMATH Keywords: critical speed
zbMATH Keywords: sharp solution
MaRDI profile type: Publication
full work available at URL: dcds.2013.33.173
OpenAlex ID: W2061756705
DOI: 10.3934/DCDS.2013.33.173
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description: scientific article; zbMATH DE number 6146681