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In this article, we investigate a hybrid model combined by a parabolic differential equation and a parabolic hemivariational inequality (so-called differential hemivariational inequality of parabolic–parabolic type) in general infinite dimensional spaces which includes the history-dependent operator. The solvability of initial value problems as well as the periodic problems of the hemivariational inequality and the differential hemivariational inequality have been proved. In application, we study a contact problem with normal compliance driven by a history-dependent dynamical system. 相似文献
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Nonconvex functions and variational inequalities 总被引:8,自引:0,他引:8
M. A. Noor 《Journal of Optimization Theory and Applications》1995,87(3):615-630
In this paper, we study some properties of a class of nonconvex functions, called semipreinvex functions, which includes the classes of preinvex functions and arc-connected convex functions. It is shown that the minimum of an arcwise directionally differentiable semi-invex functions on a semi-invex set can be characterized by a class of variational inequalities, known as variational-like inequalities. We use the auxiliary principle technique to prove the existence of a solution of a variational-like inequality and suggest a novel iterative algorithm. 相似文献
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Markku Miettinen 《Applicable analysis》2013,92(3-4):303-326
We prove the existence of a solution of a constrained hemivariational inequality, and, develop a fully discrete approximation of it. The relation between the constrained hemivariational inequality and a problem of finding substationary points of the corresponding potential function is also studied. 相似文献
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Charalambos C. Baniotopoulos Jaroslav Haslinger Zuzana Morávková 《Applications of Mathematics》2005,50(1):1-25
The paper deals with approximations and the numerical realization of a class of hemivariational inequalities used for modeling of delamination and nonmonotone friction problems. Assumptions guaranteeing convergence of discrete models are verified and numerical results of several model examples computed by a nonsmooth variant of Newton method are presented.The research was realized in the frame of the bilateral cooperation between Charles University, Prague and Aristotle University, Thessaloniki. The second author also acknowledges the support of the grant no. IAA1075402 of the Grant Agency of the Academy of Sciences of the Czech Republic and MSM 113200007.This revised version was published online in April 2005 with a corrected issue number. 相似文献
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Yunxiang Li Xiuwen Li Yiliang Liu 《Mathematical Methods in the Applied Sciences》2016,39(11):3088-3101
In this paper, we focus on the approximate controllability of control systems described by a large class of fractional evolution hemivariational inequalities. Firstly, we introduce the concept of mild solutions and present the existence of mild solutions for this kind of problems. Next, we show the approximate controllability of the corresponding linear control system. Finally, the approximate controllability of the fractional evolution hemivariational inequalities is formulated and proved under some appropriate conditions. An example demonstrates the applicability of our results. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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Solvability and optimal controls for semilinear fractional evolution hemivariational inequalities
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Liang Lu Zhenhai Liu Wei Jiang Jinlian Luo 《Mathematical Methods in the Applied Sciences》2016,39(18):5452-5464
This paper is concerned with the control systems of semilinear fractional evolution hemivariational inequalities and their optimal controls in Banach space. Firstly, the existence of mild solutions is obtained and proved mainly by using a well‐known fixed point theorem of multivalued maps and the properties of generalized Clarke subdifferential. Then, by applying generally mild conditions of cost functionals, we investigate the existence results of the optimal controls for fractional differential evolution hemivariational inequalities. Finally, an example is given to demonstrate the applicability of the main results. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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We develop a technique to obtain new symmetrization inequalities that provide a unified framework to study Sobolev inequalities, concentration inequalities and sharp integrability of solutions of elliptic equations. 相似文献
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Optimal Hardy-Rellich inequalities, maximum principle and related eigenvalue problem 总被引:1,自引:0,他引:1
In this paper we deal with three types of problems concerning the Hardy-Rellich's embedding for a bi-Laplacian operator. First we obtain the Hardy-Rellich inequalities in the critical dimension n=4. Then we derive a maximum principle for fourth order operators with singular terms. Then we study the existence, non-existence, simplicity and asymptotic behavior of the first eigenvalue of the Hardy-Rellich operator under various assumptions on the perturbation q. 相似文献
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Stephan Ramon Garcia 《Proceedings of the American Mathematical Society》2008,136(1):171-179
If is a complex symmetric operator on a separable complex Hilbert space , then the spectrum of can be characterized in terms of a certain approximate antilinear eigenvalue problem. This approach leads to a general inequality (applicable to any bounded operator ), in terms of the spectra of the selfadjoint operators and , restricting the possible location of elements of . A sharp inequality for the operator norm is produced, and the extremal operators are shown to be complex symmetric.
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In this paper, we generalize some existing discrete Gronwall-Bellman-Ou-Iang-type inequalities to more general situations. These are in turn applied to study the boundedness, uniqueness, and continuous dependence of solutions of certain discrete boundary value problem for difference equations. 相似文献
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Goeleven D. Miettinen M. Panagiotopoulos P. D. 《Journal of Optimization Theory and Applications》1999,103(3):567-601
Dynamic hemivariational inequalities are studied in the present paper. Starting from their solution in the distributional sense, we give certain existence and approximation results by using the Faedo–Galerkin method and certain compactness arguments. Applications from mechanics (viscoelasticity) illustrate the theory. 相似文献
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Exact constants in Poincaré type inequalities for functions with zero mean boundary traces
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In this paper, we investigate Poincaré type inequalities for the functions having zero mean value on the whole boundary of a Lipschitz domain or on a measurable part of the boundary. We find exact and easily computable constants in these inequalities for some basic domains (rectangles, cubes, and right triangles) and discuss applications of the inequalities to quantitative analysis of partial differential equations. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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Yongjian Liu Zhenhai Liu Dumitru Motreanu 《Mathematical Methods in the Applied Sciences》2020,43(17):9543-9556
In this paper, we consider the regularization of a class of elliptic variational-hemivariational inequalities driven by the fractional Laplace operator. First, we demonstrate characterizations of nonlocal elliptic variational-hemivariational inequalities. Next, we provide coercivity conditions that guarantee the existence and uniqueness of solution. Finally, by virtue of the so-called Browder–Tikhonov regularization method, we introduce a strongly convergent approximation procedure for the considered nonlocal problems considered without any coercivity condition. 相似文献
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Anca Capatina Marius Cocou Michel Raous 《Mathematical Methods in the Applied Sciences》2009,32(14):1804-1827
This paper deals with the mathematical and numerical analysis of a class of abstract implicit evolution variational inequalities. The results obtained here can be applied to a large variety of quasistatic contact problems in linear elasticity, including unilateral contact or normal compliance conditions with friction. In particular, a quasistatic unilateral contact problem with nonlocal friction is considered. An algorithm is derived and some numerical examples are presented. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献