On a size-structured population model with infinite states-at-birth and distributed delay in birth process

Abstract

In this article, we study a size-structured population model with infinite states-at-birth and distributed delay in birth process. We establish the well-posedness for this model and show that the solution of this model exhibits an asynchronous exponential growth by means of semigroups.

Keywords:

• size-structured populations
• distributed delay
• well-posedness
• asynchronous exponential growth
• semigroups

AMS Subject Classifications::

• 35L02
• 35P99

Acknowledgements

The authors are glad to acknowledge their gratefulness to the anonymous reviewers for valuable comments and suggestions on modifying this manuscript. This work is supported by NSF of China (11171295), NSF of Guangdong Province of China (S2011040001407, LYM10133) and NSF of Zhaoqing University.