Theory and Application of a Class of Abstract Differential-Algebraic Equations

We first provide a detailed background of a geometric projection methodology developed by Professor Roswitha März at Humboldt University in Berlin for showing uniqueness and existence of solutions for ordinary differential-algebraic equations (DAEs). Because of the geometric and operator-theoretic aspects of this particular method, it can be ex-tended to the case of infinite-dimensional abstract DAEs. For example, partial differential equations (PDEs) are often formulated as abstract Cauchy or evolution problems which we label abstract ordinary differential equations or AODE. Using this abstract formula-tion, existence and uniqueness of the Cauchy problem has been studied. Similarly, we differential-algebraic equation or ADAE problem. Existence and uniqueness of solutions DAEs. These existence and uniqueness results are then applied to some index-1 DAEs in the area of thermodynamic modeling of a chemical vapor deposition reactor and to a structural dynamics problem. The application for the structural dynamics problem, in particular, provides a detailed construction of the model and development of the DA