Convergence results for nonlinear evolution inclusions

• Autorzy: Tiziana Cardinali , Francesca Papalini
• Języki publikacji: EN

Abstrakty

EN

In this paper we consider evolution inclusions of subdifferential type. First, we prove a convergence result and a continuous dependence proposition for abstract Cauchy problem of the form u' ∈ -∂⁻f(u) + G(u), u(0) = x₀, where ∂⁻f is the Fréchet subdifferential of a function f defined on an open subset Ω of a real separable Hilbert space H, taking its values in IR ∪ {+∞}, and G is a multifunction from C([0,T],Ω) into the nonempty subsets of L²([0,T],H). We obtain analogous results for the multivalued perturbed problem x' ∈ -∂⁻f(x) + G(t,x), x(0) = x₀, where G:[0,T]×Ω → N(H) is a suitable multifunction.

Słowa kluczowe

EN

Fréchet subdifferential; convergence property; φ-monotone subdifferential of order two; solution set; Nemytski operator

Kategorie tematyczne

• 34G20: Nonlinear equations

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 1995
• Tom: 15
• Numer: 1
• Strony: 43-60

Daty

wydano

1995

Twórcy

autor

Tiziana Cardinali

• Department of Mathematics of Perugia University, Via Vanvitelli 1, Perugia 06123, Italy

autor

Francesca Papalini

• Department of Mathematics of Perugia University, Via Vanvitelli 1, Perugia 06123, Italy

Bibliografia

• [1] J. P. Aubin, A. Cellina, Differential Inclusions, Springer-Verlag, Berlin 1984.
• [2] H. Brezis, Analyse fonctionelle, théorie et applications, Masson, Paris 1983.
• [3] T. Cardinali, F. Papalini, Existence theorems for nonlinear evolution inclusions, to apper.
• [4] G. Colombo, M. Tosques, Multivalued perturbations for a class of nonlinear evolution equations, Ann. di Mat. Pura Appl. 160 (1991), pp 147-162.
• [5] J. Hale, Ordinary differential equations, Wiley-Interscience, New York 1969.
• [6] M. Tosques, Quasi-autonomous parabolic evolution equations associated with a class of nonlinear operators, Ricerche di Matematica 38 (1989), pp. 63-92.