2026-09-19T15:20:18Zhttps://ecommons.cornell.edu/server/oai/requestoai:ecommons.cornell.edu:1813/107392026-07-07T15:02:19Zcom_1813_35col_1813_47
Robinson, Michael
2008-04-25T17:51:51Z
2013-04-25T06:11:45Z
2008-04-25T17:51:51Z
https://hdl.handle.net/1813/10739
6397117
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
Floer homology
semilinear parabolic equation
blow-up behavior
IMEX method
asymptotic series
Eternal Solutions and Heteroclinic Orbits of a Semilinear Parabolic Equation
dissertation or thesis
application/pdf
Publication
Cornell Theses and Dissertations
Robinson, Michael
5893a6ea-7af3-41d7-abc6-04bcd26ab5df
COMPLETE
open.access
open.access
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<Keyword>Floer homology</Keyword>
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<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.</Abstract>
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