Parabolic problems on noncylindrical domains: the method of Rothe
2006 (English)Licentiate thesis, comprehensive summary (Other academic)
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  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.
Place, publisher, year, edition, pages
Luleå: Luleå tekniska universitet, 2006. , 96 p.
Licentiate thesis / Luleå University of Technology, ISSN 1402-1757 ; 2006:66
Research subject Mathematics
IdentifiersURN: urn:nbn:se:ltu:diva-18375Local ID: 849ee820-a0ab-11db-8975-000ea68e967bOAI: oai:DiVA.org:ltu-18375DiVA: diva2:991383
Godkänd; 2006; 20070110 (haneit)2016-09-292016-09-29Bibliographically approved