ACTA MATHEMATICA UNIVERSITATIS COMENIANAE
Vol. 65,   1   (1996)
ON THE STRUCTURE OF THE SOLUTION SET OF EVOLUTION INCLUSIONS WITH TIME-DEPENDENT SUBDIFFERENTIALS
N. S. PAPAGEORGIOU and F. PAPALINI
In this paper we consider evolution inclusions driven by a time dependent subdifferential operator and a set-valued perturbation term. First we show that the problem with a convex-valued, $h$-u.s.c. orientor field (i.e. perturbation term) has a nonempty solution set which is an $R_\delta $-set in $C(T, H)$, in particular then compact and acyclic. For the non convex problem (i.e. the orientor field is non convex-valued), without assuming that the functional $\varphi(t, x)$ of the subdifferential is of compact type, we show that for every initial datum $\xi\in \dm \varphi(0, \cdot)$ the solution set $S(\xi)$ is nonempty and we also produce a continuous selector for the multifunctions $\xi\to S(\xi)$. Some examples of distributed parameter systems are also included.
AMS subject classification.
$h$-upper semicontinuity, Hausdorff metric, subdifferential, function of compact type, parabolic problem, compact embedding
Download:     Adobe PDF     Compressed Postscript
Acta Mathematica Universitatis Comenianae
Institute of Applied
Faculty of Mathematics,
Physics and Informatics
842 48 Bratislava, Slovak Republic
Telephone: + 421-2-60295111 Fax: + 421-2-65425882
© Copyright 2001, ACTA MATHEMATICA