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A variational principle for certain dissipative evolution equations Tzou, Leo
Abstract
We formulate a variational principle which models several first order parabolic Cauchy problems. Unlike the one proposed by Brezis-Ekeland in [2], this principle does not require the identification of the extremal value, which was a major hurdle for the applicability of their approach. Our method is based on a concept of "self-duality" inherent in many parabolic evolution equations, including those driven by the gradient of a convex energy functional. The new principle is used to provide global existence and uniqueness results of solutions for the heat equation (of course) but also for quasi-linear parabolic equations, porous media and fast diffusion equations.
Item Metadata
| Title |
A variational principle for certain dissipative evolution equations
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| Creator | |
| Publisher |
University of British Columbia
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| Date Issued |
2003
|
| Description |
We formulate a variational principle which models several first order parabolic
Cauchy problems. Unlike the one proposed by Brezis-Ekeland in [2], this
principle does not require the identification of the extremal value, which was
a major hurdle for the applicability of their approach. Our method is based
on a concept of "self-duality" inherent in many parabolic evolution equations,
including those driven by the gradient of a convex energy functional. The
new principle is used to provide global existence and uniqueness results of
solutions for the heat equation (of course) but also for quasi-linear parabolic
equations, porous media and fast diffusion equations.
|
| Extent |
1513430 bytes
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| Genre | |
| Type | |
| File Format |
application/pdf
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| Language |
eng
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| Date Available |
2009-10-29
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| Provider |
Vancouver : University of British Columbia Library
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| Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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| DOI |
10.14288/1.0080076
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| URI | |
| Degree | |
| Program | |
| Affiliation | |
| Degree Grantor |
University of British Columbia
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| Graduation Date |
2003-11
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| Campus | |
| Scholarly Level |
Graduate
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| Aggregated Source Repository |
DSpace
|
Item Media
Item Citations and Data
Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.