On a prey-predator reaction-diffusion system with Holling type III functional response
type: Item
instance of: scholarly article
title: On a prey-predator reaction-diffusion system with Holling type III functional response
zbMATH Open document ID: 1205.65274
published in: Journal of Computational and Applied Mathematics
publication date: 2010-10-07T00:00:00Z
review text: The authors consider the system named in the title (characterized by prey-dependent feeding rates of the predator) as initial value problem along with Neumann-type boundary conditions in \(n\) spatial dimensions and, defining mild and strong solutions in a Banach space, prove well-posedness of strong solutions (supposing only positivity of the constants involved in the system, and regularity of the initial data), their continuous dependence on the initial values, as well as positivity and boundedness on finite time intervals. Finally, they specialize to one spatial dimension and use the fast Fourier transform coupled with classical fourth-order Runge-Kutta method in time, to obtain numerical approximations.
reviewed by: Gisbert Stoyan
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 5796765
zbMATH Keywords: reaction-diffusion equation system
zbMATH Keywords: well-posedness
zbMATH Keywords: positivity and boundedness of solutions
zbMATH Keywords: numerical approximation
zbMATH Keywords: semidiscretization
zbMATH Keywords: prey-predator reaction-diffusion system
zbMATH Keywords: Holling type III functional response
zbMATH Keywords: fast Fourier transform
zbMATH Keywords: fourth-order Runge-Kutta method
Wikidata QID: Q115581102
author: Narcisa Apreutesei
author: G. Dimitriu
describes a project that uses: Differentiation Matrix Suite
describes a project that uses: Matlab
MaRDI profile type: Publication
full work available at URL: j.cam.2010.05.040
OpenAlex ID: W2007847050
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DOI: 10.1016/J.CAM.2010.05.040
description: scientific article; zbMATH DE number 5796765