This Licentiate Thesis deals with parabolic problems on non-cylindrical domains. The existence and uniqueness of the corresponding initial- boundary value problem is proved by the method of Rothe, which - for the case of non-cylindrical domains - has to be appropriately generalized and applied. In Chapter 1 the Dirichlet problem for a linear operator of order 2k is investigated. Chapter 2 deals again with linear operators, but having some singularities at du/dt as well as in the elliptic part, which involves the use of some weighted Sobolev spaces. Chapter 3 is devoted to operators which are nonlinear in their elliptic part. In the last chapter, the so- called tranformation method, introduced in [3] and which allows to transform a parabolic problem on a non-cylindrical domain to a cylindrical one, is extended from strongly elliptic linear operators to operators, which are nonlinear and singular. / <p>Godkänd; 2006; 20070110 (haneit)</p>
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:ltu-18375 |
| Date | January 2006 |
| Creators | Kuliev, Komil |
| Publisher | Luleå tekniska universitet, Matematiska vetenskaper, Luleå |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Licentiate thesis, comprehensive summary, info:eu-repo/semantics/masterThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | Licentiate thesis / Luleå University of Technology, 1402-1757 ; 2006:66 |
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