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Uniqueness of travelling waves for nonlocal monostable equations
Author(s):
Jack
Carr;
Adam
Chmaj
Journal:
Proc. Amer. Math. Soc.
132
(2004),
2433-2439.
MSC (2000):
Primary 92D15, 39B99, 45G10
Posted:
March 4, 2004
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Abstract:
We consider a nonlocal analogue of the Fisher-KPP equation
and its discrete counterpart  ,  , and show that travelling wave solutions of these equations that are bounded between  and  are unique up to translation. Our proof requires finding exact a priori asymptotics of a travelling wave. This we accomplish with the help of Ikehara's Theorem (which is a Tauberian theorem for Laplace transforms).
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Additional Information:
Jack
Carr
Affiliation:
Department of Mathematics, Heriot-Watt University, Riccarton, Edinburgh, EH14 4AS, UK
Email:
j.carr@ma.hw.ac.uk
Adam
Chmaj
Affiliation:
Department of Mathematics, Heriot-Watt University, Riccarton, Edinburgh, EH14 4AS, UK
Address at time of publication:
Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
Email:
chmaj@math.msu.edu
DOI:
10.1090/S0002-9939-04-07432-5
PII:
S 0002-9939(04)07432-5
Received by editor(s):
August 6, 2002
Received by editor(s) in revised form:
May 7, 2003
Posted:
March 4, 2004
Additional Notes:
This work was supported by a Marie Curie Fellowship of the European Community IHP programme under contract number HPMFCT-2000-00465 and in part by NSF grant DMS-0096182
Communicated by:
Mark J. Ablowitz
Copyright of article:
Copyright
2004,
American Mathematical Society
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