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Monotone methods and attractivity results for Volterra integro-partial differential equations

Published online by Cambridge University Press:  14 November 2011

Andrea Schiaffino  and
Alberto Tesei
Andrea Schiaffino
Affiliation:
Istituto Matematico “G. Castelnuovo”, Città Universitaria, Rome, Italy
Alberto Tesei
Affiliation:
Istituto per le Applicazioni del Calcolo “M. Picone”, CNR, Rome, Italy
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Synopsis

A Volterra integro-partial differential equation of parabolic type, which describes the time evolution of a population in a bounded habitat, subject both to past history and space diffusion effects, is investigated; general homogeneous boundary conditions are admissible. Under suitable conditions, the unique nontrivial nonnegative equilibrium is shown to be globally attractive in the supremum norm. Monotone methods are the main tool of the proof.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 89 , Issue 1-2 , 1981 , pp. 135 - 142
Copyright
Copyright © Royal Society of Edinburgh 1981

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