Parabolic problems on noncylindrical domains : the method of Rothe

• 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.

Subject headings

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

Keyword

Matematik

Mathematics

Publication and Content Type

vet (subject category)

lic (subject category)