Periodic Traveling Waves for Diffusion Equations with Time Delayed and Non-local Responding Reaction

• Autores: Dawn Duehring, Wenzhang Huang
• Localización: Journal of dynamics and differential equations, ISSN 1040-7294, Vol. 19, Nº. 2, 2007, págs. 457-477
• Idioma: inglés
• DOI: 10.1007/s10884-006-9048-8
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• Resumen

  • 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.