On the convergence of solutions of
parabolic equations and applications
Z. Denkowski, denkowski(at)softlab.ii.uj.edu.pl
S. Migórski, migorski(at)softlab.ii.uj.edu.pl
Jagiellonian University, Institute of Computer Science, Nawojki 11, 30-072 Cracow, Poland
Nikolaos S. Papageorgiou, npapg(at)math.ntua.gr
National Technical University, Department of Mathematics, Zografou Campus, Athens 15780, Greece
Abstract: In this paper we examine parametric nonlinear parabolic problems with multivalued terms. Using a general notion of G-convergence for such operators we prove a convergence theorem for the solution sets of the corresponding Cauchy-Dirichlet problem. We also study a related minimax control problem.
Keywords: G-convergence, maximal monotone operator, coercive operator, existence theorem, multivalued operator, minimax problem.
The paper appeared in Nonlinear Analysis: Theory, Methods & Applications, Vol. 54, Issue 4, 2003, pp. 667-682.