An evolution inclusion driven by a time-dependent maximal monotone operator and a Lipschitz closed valued perturbation, in a separable Hilbert space is considered. The inclusion with a convexified perturbation term is...
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An evolution inclusion driven by a time-dependent maximal monotone operator and a Lipschitz closed valued perturbation, in a separable Hilbert space is considered. The inclusion with a convexified perturbation term is also studied. Then, the existence of solutions and the relaxation property between these evolution inclusions are proved. Applications to dynamical systems governed by a couple of a fractional equation and an evolution inclusion involving time-dependent maximal monotone operators with a Lipschitz perturbation are presented.
In this paper, the approximate controllability of Hilfer fractional stochastic evolution inclusion with nonlocal conditions is investigated. By using fractional calculus, semigroups theory, stochastic analysis and the...
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In this paper, the approximate controllability of Hilfer fractional stochastic evolution inclusion with nonlocal conditions is investigated. By using fractional calculus, semigroups theory, stochastic analysis and the fixed point theorem for multi-valued maps, a new sufficient condition for the existence of mild solution of the Hilfer fractional stochastic system in the space of weighted continuous functions is derived. Furthermore, a novel sufficient condition for the approximate controllability of the Hilfer fractional stochastic evolution inclusion with nonlocal conditions is established. Finally, an example is presented to illustrate the main results.
In this paper, we consider the controllability of a class of evolution inclusion in Banach space. A sufficient condition is established by using the fixed-point theorem for multi-valued.
ISBN:
(纸本)9783319676180
In this paper, we consider the controllability of a class of evolution inclusion in Banach space. A sufficient condition is established by using the fixed-point theorem for multi-valued.
For the class of nonautonomous evolution inclusions with pointwise pseudomonotone multi- valued mappings the dynamics as t -> +infinity of all global weak solutions defined on [0,+infinity) is studied. The existenc...
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ISBN:
(纸本)9783319083773;9783319083766
For the class of nonautonomous evolution inclusions with pointwise pseudomonotone multi- valued mappings the dynamics as t -> +infinity of all global weak solutions defined on [0,+infinity) is studied. The existence of a compact uniform trajectory attractor is proved. The results obtained allow one to study the dynamics of solutions for new classes of evolution inclusions related to nonlinear mathematical models of controlled geophysical and socioeconomic processes and for fields with interaction functions of pseudomonotone type satisfying the condition of polynomial growth and the standard sign condition.
The paper deals with second order nonlinear evolution inclusions and their applications. We study evolution inclusions involving a Volterra-type integral operator, which are considered within the framework of an evolu...
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The paper deals with second order nonlinear evolution inclusions and their applications. We study evolution inclusions involving a Volterra-type integral operator, which are considered within the framework of an evolution triple of spaces. First, we deliver a result on the unique solvability of the Cauchy problem for the inclusion by combining a surjectivity result for multivalued pseudomonotone operators and the Banach contraction principle. Next, we provide a theorem on the continuous dependence of the solution to the inclusion with respect to the operators involved in the problem. Finally, we consider a dynamic frictional contact problem of viscoelasticity for materials with long memory and indicate how the result on evolution inclusion is applicable to the model of the contact problem. (C) 2012 Published by Elsevier Ltd
In the finite dimensional setting, we investigate the existence of viscosity subsolutions of Hamilton-Jacobi-Bellman equations related to control problems subject to evolution inclusions governed by time-dependent max...
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In the finite dimensional setting, we investigate the existence of viscosity subsolutions of Hamilton-Jacobi-Bellman equations related to control problems subject to evolution inclusions governed by time-dependent maximal monotone operators with Young measures.
This paper considers the minimisation problem of an integral functional with an integrand and a mixed nonconvex control constraint under some suitable conditions. We minimise the integral functional on the solution se...
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This paper considers the minimisation problem of an integral functional with an integrand and a mixed nonconvex control constraint under some suitable conditions. We minimise the integral functional on the solution set of a control system described by nonlinear evolutionary inclusions with the mixed nonconvex control constraint, in which the left-hand side of the system contains the difference of two Clarke's Subdifferentials. We discuss a relaxation problem along with the original problem and show that the relaxation problem has an optimal solution, and for every optimal solution, there exists a minimising sequence of the original problem that converges to this solution concerning the trajectory, the control, and the functional.
We discuss conditions for the existence of at least one solution of semilinear evolution inclusions with a nonlocal condition and a nonconvex right-hand side. Our technique is based on fixed point theorems for multiva...
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We discuss conditions for the existence of at least one solution of semilinear evolution inclusions with a nonlocal condition and a nonconvex right-hand side. Our technique is based on fixed point theorems for multivalued maps. (C) 2009 Elsevier Ltd. All rights reserved.
In this paper, we study a class of evolution subdifferential inclusions involving history-dependent operators. We improve our previous theorems on existence and uniqueness and produce a continuous dependence result wi...
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In this paper, we study a class of evolution subdifferential inclusions involving history-dependent operators. We improve our previous theorems on existence and uniqueness and produce a continuous dependence result with respect to weak topologies under a weaker smallness condition. Two applications are provided to a frictional viscoelastic contact problem with long memory, and to a nonsmooth semipermeability problem.
We consider the identification problem of three operators having different properties for the systems governed by nonlinear second order evolution inclusions with the Volterra integral term. For the abstract identific...
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We consider the identification problem of three operators having different properties for the systems governed by nonlinear second order evolution inclusions with the Volterra integral term. For the abstract identification problem, we show the existence of optimal solutions. We provide applications to evolution hemivariational inequalities and to viscoelastic frictional contact problem of mechanics.
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