A Tikhonov-type theorem for abstract parabolic differential inclusions in Banach spaces

Anastasie Gudovich, Mikhail Kamenski, and Paolo Nistri. "A Tikhonov-type theorem for abstract parabolic differential inclusions in Banach spaces." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 21.2 (2001): 207-234. <http://eudml.org/doc/271537>.

@article{AnastasieGudovich2001,
abstract = {We consider a class of singularly perturbed systems of semilinear parabolic differential inclusions in infinite dimensional spaces. For such a class we prove a Tikhonov-type theorem for a suitably defined subset of the set of all solutions for ε ≥ 0, where ε is the perturbation parameter. Specifically, assuming the existence of a Lipschitz selector of the involved multivalued maps we can define a nonempty subset $Z_L(ε)$ of the solution set of the singularly perturbed system. This subset is the set of the Hölder continuous solutions defined in [0,d], d > 0 with prescribed exponent and constant L. We show that $Z_L(ε)$ is uppersemicontinuous at ε = 0 in the C[0,d]×C[δ,d] topology for any δ ∈ (0,d].},
author = {Anastasie Gudovich, Mikhail Kamenski, Paolo Nistri},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {singular perturbations; differential inclusions; analytic semigroups; multivalued compact operators; Lipschitz selections; singularly perturbed semilinear parabolic inclusions},
language = {eng},
number = {2},
pages = {207-234},
title = {A Tikhonov-type theorem for abstract parabolic differential inclusions in Banach spaces},
url = {http://eudml.org/doc/271537},
volume = {21},
year = {2001},
}

TY - JOUR
AU - Anastasie Gudovich
AU - Mikhail Kamenski
AU - Paolo Nistri
TI - A Tikhonov-type theorem for abstract parabolic differential inclusions in Banach spaces
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2001
VL - 21
IS - 2
SP - 207
EP - 234
AB - We consider a class of singularly perturbed systems of semilinear parabolic differential inclusions in infinite dimensional spaces. For such a class we prove a Tikhonov-type theorem for a suitably defined subset of the set of all solutions for ε ≥ 0, where ε is the perturbation parameter. Specifically, assuming the existence of a Lipschitz selector of the involved multivalued maps we can define a nonempty subset $Z_L(ε)$ of the solution set of the singularly perturbed system. This subset is the set of the Hölder continuous solutions defined in [0,d], d > 0 with prescribed exponent and constant L. We show that $Z_L(ε)$ is uppersemicontinuous at ε = 0 in the C[0,d]×C[δ,d] topology for any δ ∈ (0,d].
LA - eng
KW - singular perturbations; differential inclusions; analytic semigroups; multivalued compact operators; Lipschitz selections; singularly perturbed semilinear parabolic inclusions
UR - http://eudml.org/doc/271537
ER -