Abstract
A model for the growth of a size-structured cell population reproducing by fission into two identical daughters is formulated and analysed. The model takes the form of a linear first order partial differential equation (balance law) in which one term has a transformed argument. Using semigroup theory and compactness arguments we establish the existence of a stable size distribution under a certain condition on the growth rate of the individuals. An example shows that one cannot dispense with this condition.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 227-248 |
| Number of pages | 22 |
| Journal | Journal Of Mathematical Biology |
| Volume | 19 |
| Issue number | 2 |
| DOIs | |
| State | Published - Apr 1984 |
| Externally published | Yes |
Keywords
- Balance equation
- First-order partial differential equation
- Reproduction by fission
- Size-dependent population growth
- Stable size distribution
- Transformed arguments
ASJC Scopus subject areas
- Modeling and Simulation
- Agricultural and Biological Sciences (miscellaneous)
- Applied Mathematics