Convergence results for nonlinear evolution inclusions

Tiziana 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 -