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Convergence of a double step scheme for a class of parabolic Clarke subdifferential inclusions☆ [PDF]

Communications in Nonlinear Science and Numerical Simulation, 2021
In this paper we deal with a first order evolution inclusion involving a multivalued term generated by a Clarke subdifferential of a locally Lipschitz potential. For this problem we construct a double step time-semidiscrete approximation, known as the Rothe scheme.
Krzysztof Bartosz, Paweł Szafraniec
exaly   +6 more sources

Linear Structure of Functions with Maximal Clarke Subdifferential [PDF]

SIAM Journal on Optimization, 2019
It is hereby established that the set of Lipschitz functions $f:\mathcal{U}\rightarrow \mathbb{R}$ ($\mathcal{U}$ nonempty open subset of $\ell_{d}^{1}$) with maximal Clarke subdifferential contains a linear subspace of uncountable dimension (in particular, an isometric copy of $\ell^{\infty}(\mathbb{N})$).
Aris Daniilidis, Gonzalo Flores
exaly   +6 more sources

Evolution inclusions with Clarke subdifferential type in Hilbert space

Mathematical and Computer Modelling, 2010
The authors consider the existence of solutions for differential inclusions of the form \[ \begin{aligned} -\dot{x}(t) &\in \partial _{C}\phi (x(t))+G(t,x(t)),\\ x(0) &=x_0\end{aligned}\tag{1} \] in a real, separable Hilbert space \(H\), where \(\partial _{C}\) denotes the Clarke subdifferential.
Sitian Qin, Xiaoping Xue
exaly   +2 more sources

Nonlocal Controllability of Sobolev-Type Conformable Fractional Stochastic Evolution Inclusions with Clarke Subdifferential

Bulletin of the Malaysian Mathematical Sciences Society, 2022
AbstractIn this paper, Sobolev-type conformable fractional stochastic evolution inclusions with Clarke subdifferential and nonlocal conditions are studied. By using fractional calculus, stochastic analysis, properties of Clarke subdifferential and nonsmooth analysis, sufficient conditions for nonlocal controllability for the considered problem are ...
Hamdy M Ahmed, Maria Alessandra Ragusa, Ahmed Hamdy M   +2 more
exaly   +3 more sources

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Existence and controllability for fractional evolution inclusions of Clarke’s subdifferential type

Applied Mathematics and Computation, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhenhai Liu, Biao Zeng
exaly   +2 more sources

Optimal feedback control and controllability for hyperbolic evolution inclusions of Clarke’s subdifferential type

Computers and Mathematics With Applications, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhenhai Liu, Stanisław Migórski, Biao Zeng   +2 more
exaly   +4 more sources

Approximate controllability for stochastic evolution inclusions of Clarke’s subdifferential type

Applied Mathematics and Computation, 2016
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Liang Lu, Zhenhai Liu
exaly   +3 more sources

Clarke subdifferential for lipschitzian multivalued mappings

Cybernetics and Systems Analysis, 1992
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The Clarke and Michel-Penot Subdifferentials of the Eigenvalues of a Symmetric Matrix

Computational Optimization and Applications, 1999
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Jean-Baptiste Hiriart-Urruty, Adrian S. Lewis   +1 more
openaire   +2 more sources