| Contents |
| In this talk I will discuss the spreading properties of solutions of a prey-predator type reaction-diffusion system. This system belongs to the class of reaction-diffusion systems for which the comparison principle does not hold. For such class of systems, little has been known about the spreading properties of the solutions. Here, by a spreading property, we mean the way the solution propagates when starting from compactly supported initial data.
Among other things we show that propagation of the prey and the predator occurs with a definite spreading speed. Furthermore, quite intriguingly, the spreading speed of the prey and that of the predator are different in some situations.
Next I will discuss the behavior of solutions ``behind" the spreading fronts. If the corresponding ODE has a special type of Lyapunov function, one can show that the solution stabilizes to a steady-state. However, in a more general situation, the question is still largely open. |
|