| Autor: |
Sierżęga, Mikołaj |
| Rok vydání: |
2012 |
| Předmět: |
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| Druh dokumentu: |
Electronic Thesis or Dissertation |
| Popis: |
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. |
| Databáze: |
Networked Digital Library of Theses & Dissertations |
| Externí odkaz: |
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