On some abstract degenerate problems of parabolic type. III: Applications to linear and nonlinear problems (Q1813928)

[For part II, see Nonlinear Anal., Theory Methods Appl. 13, No. 1, 23-31 (1989; Zbl 0721.34070).] The authors consider Cauchy problems for degenerate evolution equations of the general form \[ (d/dt)(M(t)u(t))+L(t)u(t)=f(t,u(t)), \leqno (*) \] where \(f\) is nonlinear and \(M,L\) are linear (but possibly \(t\)-dependent). Using general results of their previous papers, the authors obtain existence results for a number of problems, including linear and semilinear equations, degenerate parabolic problems and abstract Navier- Stokes equations; also fully nonlinear equations are considered.