# Convergence results for nonlinear evolution inclusions

Tiziana Cardinali; Francesca Papalini

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (1995)

- Volume: 15, Issue: 1, page 43-60
- ISSN: 1509-9407

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topTiziana Cardinali, and Francesca Papalini. "Convergence results for nonlinear evolution inclusions." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 15.1 (1995): 43-60. <http://eudml.org/doc/275978>.

@article{TizianaCardinali1995,

abstract = {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.},

author = {Tiziana Cardinali, Francesca Papalini},

journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},

keywords = {Fréchet subdifferential; convergence property; φ-monotone subdifferential of order two; solution set; Nemytski operator; sequence of abstract Cauchy problems; Hilbert space; existence; continuous dependence; multivalued perturbed problem},

language = {eng},

number = {1},

pages = {43-60},

title = {Convergence results for nonlinear evolution inclusions},

url = {http://eudml.org/doc/275978},

volume = {15},

year = {1995},

}

TY - JOUR

AU - Tiziana Cardinali

AU - Francesca Papalini

TI - Convergence results for nonlinear evolution inclusions

JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization

PY - 1995

VL - 15

IS - 1

SP - 43

EP - 60

AB - 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.

LA - eng

KW - Fréchet subdifferential; convergence property; φ-monotone subdifferential of order two; solution set; Nemytski operator; sequence of abstract Cauchy problems; Hilbert space; existence; continuous dependence; multivalued perturbed problem

UR - http://eudml.org/doc/275978

ER -

## References

top- [1] J. P. Aubin, A. Cellina, Differential Inclusions, Springer-Verlag, Berlin 1984. Zbl0538.34007
- [2] H. Brezis, Analyse fonctionelle, théorie et applications, Masson, Paris 1983.
- [3] T. Cardinali, F. Papalini, Existence theorems for nonlinear evolution inclusions, to apper. Zbl0934.34054
- [4] G. Colombo, M. Tosques, Multivalued perturbations for a class of nonlinear evolution equations, Ann. di Mat. Pura Appl. 160 (1991), pp 147-162. Zbl0752.34013
- [5] J. Hale, Ordinary differential equations, Wiley-Interscience, New York 1969. Zbl0186.40901
- [6] M. Tosques, Quasi-autonomous parabolic evolution equations associated with a class of nonlinear operators, Ricerche di Matematica 38 (1989), pp. 63-92. Zbl0736.47026

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