Abstract
The stability of stationary solutions of the non-local reaction-diffusion equation with homogeneous Neumann boundary conditions is studied. Depending on a, bounds on the dimension of the unstable manifold of a stationary solution are given. In particular, it is shown that only constant or monotone stationary solutions may be stable. For the specific case of a cubic like f, the existence of a Hopf bifurcation is proven. Finally, some related equations are discussed. © 1995 Oxford University Press.
| Original language | English |
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| Pages (from-to) | 557-582 |
| Number of pages | 26 |
| Journal | Quarterly Journal of Mechanics and Applied Mathematics |
| Volume | 48 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - Nov 1995 |