Quasi-autonomous parabolic evolution equations associated with a class of non linear operators (Q1814204)

Let \(A\) be a nonlinear multivalued operator on a Hilbert space \(H\), \(h\) a function with values in \(H\). The author defines the strong solution of the problem \({\mathcal U}'+{\mathcal AU}\ni h\), proves a local existence theorem and a theorem characterizing the maximal interval of existence of a strong solution. In particular, the case when \(A\) is the subdifferential of a function is examined.