Eternal solutions and heteroclinic orbits of a semilinear parabolic equation
| dc.creator | Robinson, Michael | |
| dc.date | 2008-04-30 | |
| dc.date.accessioned | 2026-07-07T09:36:06Z | |
| dc.date.available | 2026-07-07T09:36:06Z | |
| dc.description | This dissertation describes the space of heteroclinic orbits for a class of semilinear parabolic equations, focusing primarily on the case where the nonlinearity is a second degree polynomial with variable coefficients. Along the way, a new and elementary proof of existence and uniqueness of solutions is given. Heteroclinic orbits are shown to be characterized by a particular functional being finite. A novel asymptotic-numeric matching scheme is used to uncover delicate bifurcation behavior in the equilibria. The exact nature of this bifurcation behavior leads to a demonstration that the equilibria are degenerate critical points in the sense of Morse. Finally, the space of heteroclinic orbits is shown to have a cell complex structure, which is finite dimensional when the number of equilibria is finite. | |
| dc.description | 170 pages, many figures | |
| dc.identifier | https://arxiv.org/abs/0804.4883 | |
| dc.identifier | http://arxiv.org/abs/0804.4883 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/160054 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37L05; 35B40 | |
| dc.title | Eternal solutions and heteroclinic orbits of a semilinear parabolic equation | |
| dc.type | text |