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

Anastasie Gudovich; Mikhail Kamenski; Paolo Nistri

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2001)

- Volume: 21, Issue: 2, page 207-234
- ISSN: 1509-9407

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topAnastasie 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 -

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