Doctor of Philosophy
In using dynamic or Wentzell boundary conditions in parabolic and hyperbolic problems in partial differential equations, a positive function beta on the boundary of the underlying domain arises naturally. The relevant space of functions on the boundary is L2(on the boundary with weight). In all previous studies, beta was positive, continuous, and both beta and 1/beta were bounded. In this thesis, beta is merely positive and Lebesgue measurable. In particular, both beta and 1/beta can be essentially unbounded. The construction of the appropriate selfadjoint operator on the L2 space involving both omega and its boundary is based on quadratic form methods. The allows for more general coefficients in the basic elliptic operators. This leads to new wellposedness results which are applied to give significant extentions of recent asymptotic parabolicity results for strongly damped wave equations.
Dissertation or thesis originally submitted to the local University of Memphis Electronic Theses & dissertation (ETD) Repository.
Clendenen, Raluca Ioana Pop, "Wentzell Boundary Conditions with General Weights and Asymptotic Parabolicity for Strongly Damped Waves." (2014). Electronic Theses and Dissertations. 944.