A sequence of order relations, encoding heteroclinic connections in scalar parabolic PDE
- Wolfrum, Matthias
2010 Mathematics Subject Classification
- 35K57 37L30 35B41 34C37
- calar semilinear parabolic PDE, order structures; attractors, heteroclinic connections, meandric permutations, nodal properties
ut = uxx + ƒ (x, u, ux), 0 < x < 1
on a bounded interval with Neumann conditions. Introducing a sequence of order relations, we prove a new and simple criterion for the existence of heteroclinic connections, using only information about nodal properties of solutions to the stationary ODE problem. This result allows also for a complete classiffication of possible attractors in terms of the permutation of the equilibria, given by their order at the two boundaries of the interval.
- J. Differential Equations, 183, (2002) pp. 56-78