Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9501639 | Journal of Differential Equations | 2005 | 25 Pages |
Abstract
We present a hierarchically size-structured population model with growth, mortality and reproduction rates which depend on a function of the population density (environment). We present an example to show that if the growth rate is not always a decreasing function of the environment (e.g., a growth which exhibits the Allee effect) the emergence of a singular solution which contains a Dirac delta mass component is possible, even if the vital rates of the individual and the initial data are smooth functions. Therefore, we study the existence of measure-valued solutions. Our approach is based on the vanishing viscosity method.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Azmy S. Ackleh, Kazufumi Ito,