Browsing by Author "Ali Eshetu"

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    Varational Formulation of Elliptic Partial Differential Equation
    (Addis Ababa University, 2024-07) Ali Eshetu; Tsegaye Gedif
    The focus of this thesis is to examine weak or variational formulations of various elliptic boundary value problems and determine whether or not they are well-posed. The weak version of the homogeneous Dirichlet boundary value problem for the Poisson equation is first derived. A weak formulation can be thought of as an operator equation in its abstract form. Additionally, we offer some broad conclusions on the existence and uniqueness of linear operator equations.