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Existence-uniqueness and long time behavior for a class of nonlocal nonlinear parabolic evolution equations
Author(s):
Azmy
S.
Ackleh;
Lan
Ke
Journal:
Proc. Amer. Math. Soc.
128
(2000),
3483-3492.
MSC (2000):
Primary 35K50, 35K55, 35K99, 35B40, 92D25
Posted:
August 17, 2000
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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:
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
Posted:
August 17, 2000
Communicated by:
David S. Tartakoff
Copyright of article:
Copyright
2000,
American Mathematical Society
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