Evolution in a Changing Environment: Existence of Solutions

P. Rybka*, Q. Tang† and D. Waxman‡

Colloquium Mathematicum 98, 97-111 (2003)

*Institute of Applied Mathematics and Mechanics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland
†School of Mathematical Sciences, University of Sussex, Brighton BN1 9QH, UK
‡Centre for the Study of Evolution, School of Life Sciences, University of Sussex, Falmer, Brighton BN1 9QG, United Kingdom

We establish the existence of solutions of an intrinsically nonlinear differential-integral equation that arises from the mathematical modelling of the evolution of an asexual population in a changing environment. The main objective is to pave the way for a rigorous analysis of the linear stability of travelling wave solutions of the corresponding problem.