Geodesic
Evolution parabolic inequalities with multivalued operators
Sbornik. Mathematics, Tome 79 (1994) no. 2, pp. 365-380 
V. S. Klimov. Evolution parabolic inequalities with multivalued operators. Sbornik. Mathematics, Tome 79 (1994) no. 2, pp. 365-380. http://geodesic.mathdoc.fr/item/SM_1994_79_2_a7/
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     url = {http://geodesic.mathdoc.fr/item/SM_1994_79_2_a7/}
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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.

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