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Topics in the theory of semilinear heat equations
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Sierżęga, Mikołaj (2012) Topics in the theory of semilinear heat equations. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b2583526~S1
Abstract
We present new techniques and results in the theory of existence and regularity of
solutions to semilinear heat equations with singular initial data.
We review the standard well-posedness theory for the equation with the power nonlinearity
and initial data in Lebesgue spaces and argue that there is a need for a different
approach to proving existence of classical solutions. Next, an existence theory based on
the concept of supersolutions is developed. A theory of construction of supersolutions is
provided and applied to a selection of model examples. We conclude the discussion of supersolutions
with a new and more general proof of the local and global existence of classical
solutions for the equation with the power nonlinearity in the critical space.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Heat equation | ||||
Official Date: | March 2012 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Robinson, James C. (James Cooper), 1969- | ||||
Sponsors: | Engineering and Physical Sciences Research Council (EPSRC) (EP/G007470/1) | ||||
Extent: | vii, 116 leaves | ||||
Language: | eng |
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