This work presents a detailed study of linear abstract degenerate differential equations, using both the semigroups generated by multivalued (linear) operators and extensions of the operational method from Da Prato and Grisvard. The authors describe the recent and original results on PDEs and algebraic-differential equations, and establishes the analyzability of the semigroup generated by some degenerate parabolic operators in spaces of continuous functions.

Preliminaries and notations; multivalued linear operators; degenerate equations of hyperbolic type; degenerate equations of parabolic type I; degenerate equations of parabolic type II; degenerate equations - the general case; degenerate differential equations of the second order; degenerate parabolic equations; bibliographical remarks.