Global existence of solutions and uniform persistence of a diffusive predator-prey model with prey-taxis
type: Item
instance of: scholarly article
title: Global existence of solutions and uniform persistence of a diffusive predator-prey model with prey-taxis
zbMATH Open document ID: 1335.35131
author: Sainan Wu
author: Junping Shi
author: Boying Wu
published in: Journal of Differential Equations
publication date: 2016-02-08T00:00:00Z
review text: The work deals with the question of equation-based conditions, which define the existence of solutions for the distributed predator-prey model with the taxis term included into the PDE related to the predators' dynamics. The title of the article may be slightly ambiguous: ``prey-taxis'' does not mean a taxis of preys under any stimulus but the taxis of predators induced by the gradient of preys distribution, i.e., the reaction-diffusion equation for predator density \(u\) contains an additional term \(-\chi\nabla(q(u)\nabla v)\), where \(v\) is the prey density, \(q(u)\) is some function of the predator density, and \(\chi\) is the taxis coefficient. The last quantity is the main control parameter, which determines the existence of a unique global classical solution to the system. The proven theorem determines its boundaries as an explicit expression, which depends on the space dimensionality, the diffusion coefficient for preys, and their maximal density.
reviewed by: Eugene Postnikov
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35K59
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 6539951
zbMATH Keywords: reaction-diffusion system
zbMATH Keywords: taxis
zbMATH Keywords: predator-prey model
zbMATH Keywords: global existence
zbMATH Keywords: boundedness
zbMATH Keywords: uniform persistence
MaRDI profile type: Publication
full work available at URL: j.jde.2015.12.024
OpenAlex ID: W2309615748
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Global existence of solutions and uniform persistence of a diffusive predator-prey model with prey-taxis (cites work)
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Global existence of solutions and uniform persistence of a diffusive predator-prey model with prey-taxis (cites work)
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Global existence of solutions and uniform persistence of a diffusive predator-prey model with prey-taxis (DOI)
DOI: 10.1016/J.JDE.2015.12.024