• Journal of applied mathematics & informatics
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• v.3 no.2
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• pp.279-290
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• 1996

In the present paper we study the Cauchy problem in a Banach space E for an abstract nonlinear differential equation of form $$\frac{d^2u}{dt^2}=-A{\frac{du}{dt}}+B(t)u+f(t, W)$$ where W=($A_1$(t)u, A_2(t)u)..., A_{\nu}(t)u), A_{i}(t),\;i=1,2,...{\nu}$,(B(t), t{\in}I$=[0, b]) are families of closed operators defined on dense sets in E into E, f is a given abstract nonlinear function on $I{\times}E^{\nu}$ into E and -A is a closed linar operator defined on dense set in e into E which generates a semi-group. Further the existence and uniqueness of the solution of the considered Cauchy problem is studied for a wide class of the families ($A_{i}$(t), i =1.2...${\nu}$), (B(t), $t{\in}I$) An application and some properties are also given for the theory of partial diferential equations.

• East Asian mathematical journal
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• v.26 no.5
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• pp.681-691
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• 2010

A system of variational inclusions with (A, ${\eta}$, m)-accretive operators in real q-uniformly smooth Banach spaces is introduced. Using the resolvent operator technique associated with (A, ${\eta}$, m)-accretive operators, we prove the existence and uniqueness of solutions for this system of variational inclusions and propose a Mann type iterative algorithm for approximating the unique solution for the system of variational inclusions.

• Bulletin of the Korean Mathematical Society
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• v.39 no.4
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• pp.589-606
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• 2002

We introduce and analyze a frequency-domain method for parabolic partial differential equations. The method is naturally parallelizable. After taking the Fourier transformation of given equations in the space-time domain into the space-frequency domain, we propose to solve an indefinite, complex elliptic problem for each frequency. Fourier inversion will then recover the solution in the space-time domain. Existence and uniqueness as well as error estimates are given. Fourier invertibility is also examined. Numerical experiments are presented.

• Journal of the Korean Mathematical Society
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• v.40 no.2
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• pp.195-205
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• 2003

In this paper, we introduce and study a new class of generalized strongly nonlinear variational inequalities with setvalued mappings. By using the KKM technique, we prove the existence and uniqueness of solution for this class of generalized setvalued strongly nonlinear variational inequalities in reflexive Banach spaces. Our results include the main results of Verma ［16］, ［17］ as special cases.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.1
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• pp.13-27
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• 2018

By using of the Banach fixed point theorem, the theory of a strongly continuous semigroup of operators and resolvent operator, we investigate the existence and uniqueness of S-asymptotically ${\omega}-periodic$ mild solutions for some differential (integrodifferential) equations with piecewise constant argument when specially ${\omega}$ is an integer.

• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.637-669
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• 2024

The goal of this paper is to study decay properties of weak solutions to Cauchy problem of the non-stationary fractional Navier-Stokes equations. By using the Fourier splitting method, we give the time L²-decay rate of weak solutions, which reveals that L²-decay is generally determined by its linear generalized Stokes flow. In second part, we establish various decay results and the uniqueness of the two dimensional fractional Navier-Stokes flows. In the end of this article, as an appendix, the existence of global weak solutions is given by making use of Galerkin' method, weak and strong compact convergence theorems.

• Journal of Communications and Networks
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• v.16 no.2
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• pp.121-129
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• 2014

The trend of an increasing demand for a high-quality user experience, coupled with a shortage of radio resources, has necessitated more advanced wireless techniques to cooperatively achieve the required quality-of-experience enhancement. In this study, we investigate the critical problem of rate splitting in heterogeneous cellular networks, where concurrent transmission, for instance, the coordinated multipoint transmission and reception of LTE-A systems, shows promise for improvement of network-wide capacity and the user experience. Unlike most current studies, which only deal with spectral efficiency enhancement, we implement an optimal rate splitting strategy to improve both spectral efficiency and energy efficiency by exploring and exploiting cooperation diversity. First, we introduce the motivation for our proposed algorithm, and then employ the typical cooperative bargaining game to formulate the problem. Next, we derive the best response function by analyzing the dual problem of the defined primal problem. The existence and uniqueness of the proposed cooperative bargaining equilibrium are proved, and more importantly, a distributed algorithm is designed to approach the optimal unique solution under mild conditions. Finally, numerical results show a performance improvement for our proposed distributed cooperative rate splitting algorithm.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.10 no.9
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• pp.4188-4206
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• 2016

Power control is widely used to reduce co-channel interference in wireless networks and guarantee the signal-to-interference plus noise ratio (SINR) of ongoing connections. This technique is also effective for wireless body area networks (WBANs). Although achieving satisfactory SINR is important for WBAN users, they may not be willing to achieve it at arbitrarily high power levels since power is a scarce resource in WBANs. Besides, for WBANs with different purposes, the QoS requirements and concern about the power consumption may be different. This motivates us to formulate the power control problem using the concepts from microeconomics and game theory. In this paper, the QoS objective is viewed as a utility function, which represents the degree of user satisfaction, while the power consumption is viewed as a cost function. The power control problem consequently becomes a non-cooperative multiplayer game, in which each player tries to maximize its net utility, i.e., the utility minus the cost. Within this framework, we investigate the Nash equilibrium existence and uniqueness in the game and derive the best response solution to reach the Nash equilibrium. To obtain the optimal transmission power in a distributed way, we further propose a utility-based and QoS-aware power control algorithm (UQoS-PCA). Tunable cost coefficient in UQoS-PCA enables this scheme to be flexible to satisfy diverse service requirements. Simulation results show the convergence and effectiveness of the proposed scheme as well as improvements over existing algorithm.

• Journal of Communications and Networks
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• v.18 no.4
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• pp.589-599
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• 2016

Most existing resource management problem models arise from the original desire of allocating resources in either a user-centric or network-centric manner. The difference between their objectives is obvious: user-centric methods attempt to optimize the utility of individual users, whereas network-centric models intend to optimize the collective utilities of the entire network. In this paper, from the above two aspects, we analyze the robust power control problem in device-to-device (D2D) communication underlaying cellular networks, where two types of channel uncertainty set (e.g., ellipsoidal and column-wise) are considered. In the user-centric method, we formulate the problem into the form of a Stackelberg game, where the energy efficiency (EE) of each user is the ingredient of utility function. In order to protect the cellular user equipment's (CUE) uplink transmission, we introduce a price based cost function into the objectives of D2D user equipment (DUE). The existence and uniqueness of the game with the influence of channel uncertainty and price are discussed. In the network-centric method, we aim to maximize the collective EE of CUEs and DUEs. We show that by the appropriate mathematical transformation, the network-centric D2D power control problem has the identical local solution to that of a special case of the user-centric problem, where price plays a key role. Numerical results show the performance of the robust power control algorithms in the user-centric and network-centric models.