Measure-valued solutions for a hierarchically size-structured population |
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Authors: | Azmy S Ackleh |
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Institution: | a Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504-1010, USA b Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, USA |
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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. |
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Keywords: | 35A05 35D05 35F25 35L67 92D25 |
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