Topics in the theory of semilinear heat equations
Sierżęga, Mikołaj (2012) Topics in the theory of semilinear heat equations. PhD thesis, University of Warwick.Full text not available from this repository.
Official URL: http://webcat.warwick.ac.uk/record=b2583526~S1
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|
|Institution:||University of Warwick|
|Theses Department:||Mathematics Institute|
|Supervisor(s)/Advisor:||Robinson, James C. (James Cooper), 1969-|
|Sponsors:||Engineering and Physical Sciences Research Council (EPSRC) (EP/G007470/1)|
|Extent:||vii, 116 leaves|
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