| Abstract: |
| In this talk we will discuss the dynamics of solutions of one-dimensional reaction-diffusion equations, where space-time transitions from one equilibrium to another typically occur. We will consider the general case when the profile of the propagation is not characterized by a single front, but by a layer of several fronts. This means, intuitively, that transition between equilibria may occur in several successive steps involving intermediate stationary states. In joint works with Arnaud Ducrot and Hiroshi Matano, we deal with such a situation by using the so-called zero number argument, which consists in using the number of zeros of the solution (of a linear parabolic equation) as a discrete Lyapunov function. We will show that the large-time behavior of solutions is described by a family of travelling fronts which we call a propagating terrace. |
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