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Title: Topics in the theory of semilinear heat equations
Author: Sierżęga, Mikołaj
ISNI:       0000 0004 2726 4022
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2012
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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.
Supervisor: Not available Sponsor: Engineering and Physical Sciences Research Council (EPSRC) (EP/G007470/1)
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics