Abstract:
Conditions are found under which the set of solutions of an evolution parabolic inequality is nonempty, compact, and connected. Included in the study is the Cauchy problem $f\in y'+Ay$, $y(\alpha)=h$ with a multivalued and monotone operator $A\colon Z^*\to Z$, where $Z$ is a nonreflexive $B$-space. Questions connected with well-posedness of the Cauchy problem and convergence of Faedo–Galërkin approximations are investigated.
Fulltext:
PDF file (1608 kB)