Traveling waves for the diusive Nicholson's blow¯ies equation q Joseph W.-H. So a , Xingfu Zou b, * a DepartmentofMathematicalSciences,UniversityofAlberta,Edmonton,Alberta,CanadaT6G2G1 b Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, Newfoundland, Canada A1C 5S7 Abstract We consider traveling wave front solutions for the diusive Nicholson's blow¯ies equation on the real line. The existence of such solutions is proved using the technique developed by J. Wu and X. Zou J. Dyn. Dier. Equations 13 3) 2001)). Some nu- merical simulation using the iteration formula of Wu and Zou [7] is also provided. Crown Copyright Ó 2001 Published by Elsevier Science Inc. All rights reserved. Keywords: Traveling wave front; Diusive Nicholson's blow¯ies equation; Upper-lower solution; Iteration 1. Introduction Consider the reaction±diusion equation with a discrete time delay oN t; x ot o 2 N t; x ox 2 dN t; x pN t s; xe aN ts;x ; 1 where x 2 R and t P 0. Such an equation had been studied in [4,5,8]. For the case when there is no spatial dependence, the corresponding delay equation was referred to as Nicholsons's blow¯ies equation, cf. [1] after the experiments of Nicholson [2,3] had been extensively studied. Eq. 1) can be derived based on www.elsevier.com/locate/amc Applied Mathematics and Computation 122 2001) 385±392 q Research partially supported by Natural Sciences and Engineering Research Council of Canada. * Corresponding author. E-mail addresses: joseph.so@ualberta.ca J.W.-H. So), xzou@math.mun.ca X. Zou). 0096-3003/01/$ - see front matter Crown Copyright Ó 2001 Published by Elsevier Science Inc. All rights reserved. PII:S0096-300300)00055-2