Abstract
A parabolic system with nonlinear local or nonlocal interactions is considered, with specific applications to the description of competition/combat situations. Global existence and comparison results are proven under suitable assumptions on the interaction terms. Comparisons with solutions of the 'equivalent' ordinary differential (space-independent) model that has been previously used in modelling combat are of special interest. The stationary state of such a system- corresponding to a stalemate- is also considered. Under certain conditions on the interaction, domain size, and boundary conditions, a uniqueness result is obtained for the stationary state. A simple example shows that these conditions are sharp and uniqueness may be lost when they are not fulfilled.
Original language | English (US) |
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Pages (from-to) | 285-298 |
Number of pages | 14 |
Journal | IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications) |
Volume | 44 |
Issue number | 3 |
DOIs | |
State | Published - Dec 1 1990 |
ASJC Scopus subject areas
- Applied Mathematics