TY - JOUR
T1 - Uniqueness of travelling waves for nonlocal monostable equations
AU - Carr, Jack
AU - Chmaj, Adam
PY - 2004/8
Y1 - 2004/8
N2 - We consider a nonlocal analogue of the Fisher-KPP equation ut = J * u - u + f(n), x ? R, f(0) = f(1) = 0, f > 0 on (0, 1), and its discrete counterpart u?n = (J * u)n - u n + f(un), n ? Z, and show that travelling wave solutions of these equations that are bounded between 0 and 1 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).
AB - We consider a nonlocal analogue of the Fisher-KPP equation ut = J * u - u + f(n), x ? R, f(0) = f(1) = 0, f > 0 on (0, 1), and its discrete counterpart u?n = (J * u)n - u n + f(un), n ? Z, and show that travelling wave solutions of these equations that are bounded between 0 and 1 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).
UR - http://www.scopus.com/inward/record.url?scp=3142699474&partnerID=8YFLogxK
U2 - 10.1090/S0002-9939-04-07432-5
DO - 10.1090/S0002-9939-04-07432-5
M3 - Article
VL - 132
SP - 2433
EP - 2439
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
SN - 0002-9939
IS - 8
ER -