Eternal Solutions and Heteroclinic Orbits of a Semilinear Parabolic Equation
| dc.contributor.author | Robinson, Michael | |
| dc.date.accessioned | 2008-04-25T17:51:51Z | |
| dc.date.available | 2013-04-25T06:11:45Z | |
| dc.date.issued | 2008-04-25T17:51:51Z | |
| dc.description.abstract | 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. | en_US |
| dc.identifier.other | bibid: 6397117 | |
| dc.identifier.uri | https://hdl.handle.net/1813/10739 | |
| dc.language.iso | en_US | en_US |
| dc.subject | Floer homology | en_US |
| dc.subject | semilinear parabolic equation | en_US |
| dc.subject | blow-up behavior | en_US |
| dc.subject | IMEX method | en_US |
| dc.subject | asymptotic series | en_US |
| dc.title | Eternal Solutions and Heteroclinic Orbits of a Semilinear Parabolic Equation | en_US |
| dc.type | dissertation or thesis | en_US |
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