Sierżęga, Mikołaj (2012) Topics in the theory of semilinear heat equations. PhD thesis, University of Warwick.

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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 or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Heat equation
Date:	March 2012
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Publication Status:	Unpublished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
URI:	http://wrap.warwick.ac.uk/id/eprint/50452

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