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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Existence-uniqueness and long time behavior for a class of nonlocal nonlinear parabolic evolution equations


Authors: Azmy S. Ackleh and Lan Ke
Journal: Proc. Amer. Math. Soc. 128 (2000), 3483-3492
MSC (2000): Primary 35K50, 35K55, 35K99, 35B40, 92D25
Published electronically: August 17, 2000
MathSciNet review: 1778276
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Abstract | References | Similar Articles | Additional Information

Abstract:

We establish existence and uniqueness of solutions for a general class of nonlocal nonlinear evolution equations. An application of this theory to a class of nonlinear reaction-diffusion problems that arise in population dynamics is presented. Furthermore, conditions on the initial population density for this class of problems that result in finite time extinction or persistence of the population is discussed. Numerical evidence corroborating our theoretical results is given.


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Additional Information

Azmy S. Ackleh
Affiliation: Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504-1010
Email: ackleh@louisiana.edu

Lan Ke
Affiliation: Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504-1010
Email: ke@louisiana.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05912-8
PII: S 0002-9939(00)05912-8
Keywords: Nonlocal parabolic evolution equations, unbounded diffusion, population dynamics, asymptotic behavior, extinction, persistence
Received by editor(s): July 20, 1998
Published electronically: August 17, 2000
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2000 American Mathematical Society