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1
Content available Control and optimization of abstract continuous time evolution inclusions
Mokhtar-Kharroubi Hocine
Control and Cybernetics
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2023
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Vol. 52, No. 1
5--34
EN
Abstract controlled evolution inclusions are revisited in the Banach spaces setting. The existence of solution is established for each selected control. Then, the input–output (or, control-states) multimap is examined and the Lipschitz continuous well posedness is derived. The optimal control of such inclusions handled in terms of a Bolza problem is investigated by means of the so-called PF format of optimization. A strong duality is provided, the existence of an optimal pair is given and the system of optimalty is derived. A Fenchel duality is built and applied to optimal control of convex process of evolution. Finally, it will be shown how the general theory we provided can be applied to a wide class of controled integrodifferental inclusions.
2
Content available remote Coupled fixed point theorems under new coupled implicit relation in Hilbert spaces
Kim Kyung Soo
Demonstratio Mathematica
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2022
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Vol. 55, nr 1
81--89
EN
The aim of this paper is to study existence and uniqueness of coupled fixed point for a family of self-mappings satisfying a new coupled implicit relation in a Hilbert space. We also prove well-posedness of a coupled fixed point problem.
3
Content available remote On the well-posedness of the time-differential three-phase-lag thermoelasticity model
D'Apice C., Chirita S., Zampoli V.
Archives of Mechanics
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2016
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Vol. 68, nr 5
371--393
EN
This paper analyzes the time differential three-phase-lag model of coupled thermoelasticity. The uniqueness and continuous dependence results are established for the solutions of the corresponding initial boundary value problems associated with the model in concern. The key tool of the method is to associate with the basic initial boundary value problem of the model an appropriate auxiliary initial boundary value problem and then to establish an identity of Lagrange type. This last identity is used to analyze the uniqueness of solutions under appropriate mild restrictions assumed upon the constitutive coefficients and upon the delay times. Uniqueness question is also discussed for a set of models of thermoelasticity developed in literature. Further, for the continuous dependence problem an appropriate estimate of the solution is obtained in terms of the given data. This expresses the continuous dependence of solution with respect to the initial data and with respect to the given supply loads, provided some appropriate constitutive assumptions are considered. These results give information upon the well-posedness of the time differential three-phase-lag model of coupled thermoelasticity.
4
Content available remote Addendum to: Qualitative aspects of solutions in resonators
Quintanilla R., Racke R.
Archives of Mechanics
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2011
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Vol. 63, nr 4
429-435
EN
In correcting a small mistake in [10], we can prove a new result on nonexponential stability for a coupled system arising in resonators. This also gives another (surprising and simple) example for a thermoelastic system changing from exponential stability to non-exponential stability, when changing from Fourier’s law to Cattaneo’s law in modeling of the heat conduction.
5
Content available remote Well-posedness of the fixed point problem for ø-max-contractions
Akkouchi M.
Fasciculi Mathematici
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2010
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Nr 45
5-12
EN
We study the well-posedness of the fixed point problem for self-mappings of a metric space which are ø-max-contractions (see [6]).
6
Content available remote A fixed point result for φ-contractions on b-metric spaces without the boundedness assumption
Păcurar M.
Fasciculi Mathematici
|
2010
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Nr 43
127-137
EN
Starting from a result in [V. Berinde,Generalized contractions in quasimetric spaces, Seminar on Fixed Point Theory (Preprint), "Babeş-Bolyai" University of Cluj-Napoca, 3 (1993), 3-9 ], we prove the existence and uniqueness of the fixed points for φ-contractions on b-metric spaces. We also build a theory of this fixed point result.
7
Content available remote Well-posedness of fixed point problem for mappings satisfying an implicit relation
Akkouchi M., Popa V.
Demonstratio Mathematica
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2010
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Vol. 43, nr 4
923-929
EN
The notion of well-posedness of a fixed point problem has generated much interest to a several mathematicians, for example, F. S. De Blassi and J. Myjak (1989), S. Reich and A. J. Zaslavski (2001), B. K. Lahiri and P. Das (2005) and V. Popa (2006 and 2008). The aim of this paper is to prove for mappings satisfying some implicit relations in orbitally complete metric spaces, that fixed point problem is well-posed.
8
Content available Porous sets for mutually nearest points in Banach spaces
Li C., Myjak J
Opuscula Mathematica
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2008
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Vol. 28, no. 1
73-82
EN
Let B(X) denote the family of all nonempty closed bounded subsets of a real Banach space X, endowed with the Hausdorff metric. For E, F ∈ B (X) we set [formula]. Let D denote the closure (under the maximum distance) of the set of all (E, F) ∈ B (X) x B (X) such that λE,F > 0. It is proved that the set of all (E, F) ∈ D for which the minimization problem [formula] fails to be well posed in a σ-porous subset of D.
9
Content available remote Qualitative aspects of solutions in resonators
Quintanilla R., Racke R.
Archives of Mechanics
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2008
|
Vol. 60, nr 4
345-360
EN
We consider the system of micro-beam resonators in the thermoelastic theory of Lord and Shulmann. First, we prove the uniqueness and instability of solutions when the sign of a parameter is not prescribed. Existence of solutions and uniform bounds for the real part of the spectrum have been found. We finish the paper by proving the impossibility of the time localization of solutions.
10
Content available remote Well-posedness and porosity of a certain class of operators
Lahiri B., Das P.
Demonstratio Mathematica
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2005
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Vol. 38, nr 1
169--176
EN
We prove that several fixed point problems are well-posed and study the porosity behaviour of a certain class of operators.
11
Content available Control problems for systems described by hemivariational inequalities
Denkowski Z.
Control and Cybernetics
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2002
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Vol. 31, no 3
713-738
EN
The paper considers some control problems for the systems described by the evolution, as well as the stationary hemivariational inequalities (HVIs for short). First, basing on surjectivity theorems for pseudo-monotone operators we formulate some existence results for the solutions of the HVIs and investigate some properties of the solution set (like sensitivity; i.e. its dependence on data and operators). Next we quote some existence theorems for optimal solutions for various classes of optimal control like distributed control (e.g. Bolza problem), identification of parameters, or optimal shape design for systems described by HVIs. Finally, we discuss some common features in getting the existence of optimal solutions as well as some "well-posedness" problems.
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