期刊
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
卷 19, 期 2, 页码 457-477出版社
SPRINGER
DOI: 10.1007/s10884-006-9048-8
关键词
reaction-diffusion equations; time delayand non-local response; periodic traveling waves; singular perturbation; integral equations
We develop a singular perturbation technique to study the existence of periodic traveling wave solutions with large wave speed for a class of reaction-diffusion equations with time delay and non-local response. Unlike the classical singular perturbation method, our approach is based on a transformation of the differential equations to integral equations in a Banach space that reduces the singular perturbation problem to a regular perturbation problem. The periodic traveling wave solutions then are obtained by the use of Liapunov-Schmidt method and a generalized implicit function theorem. The general result obtained has been applied to a non-local reaction-diffusion equation derived from an age-structured population model with a logistic type of birth function.
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