In this chapter we present several applications of general theory to nonlinear dynamics governed by partial differential equations of dissipative type illustrating the ideas and general existence theory developed in the previous section. Most of significant dynamics described by partial differential equations can be written in the abstract form (4.1) with appropriate quasi-
and Banach space
. The boundary value conditions are incorporated in the domain of
. The whole strategy is to find the appropriate operator
and to prove that it is quasi-
-accretive. The main emphasis here is on parabolic-like boundary value problems and the nonlinear hyperbolic equations although the area of problems covered by general theory is much larger.