• Journal of the Korean Mathematical Society
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• v.57 no.1
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• pp.215-247
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• 2020

In this paper, we deal with a two-species chemotaxis-Stokes system with Lotka-Volterra competitive kinetics under homogeneous Neumann boundary conditions in a general three-dimensional bounded domain with smooth boundary. Under appropriate regularity assumptions on the initial data, by some L^p-estimate techniques, we show that the system possesses at least one global and bounded weak solution, in addition to discussing the asymptotic behavior of the solutions. Our results generalizes and improves partial previously known ones.

• Korean Journal of Mathematics
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• v.21 no.2
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• pp.117-124
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• 2013

We investigate the existence of weak solutions for the biharmonic boundary value problem with nonlinear term decaying at the origin. We get a theorem which shows the existence of nontrivial solutions for the biharmonic boundary value problem with nonlinear term decaying at the origin. We obtain this result by reducing the biharmonic problem with nonlinear term to the biharmonic problem with bounded nonlinear term and then approaching the variational method and using the mountain pass geometry for the reduced biharmonic problem with bounded nonlinear term.

• Journal of the Korean Mathematical Society
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• v.53 no.1
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• pp.161-185
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• 2016

We consider a mathematical model which describes the quasistatic frictional contact between a piezoelectric body and an electrically conductive obstacle, the so-called foundation. A nonlinear electro-viscoelastic constitutive law is used to model the piezoelectric material. Contact is described with Signorini's conditions and a version of Coulomb's law of dry friction in which the adhesion of contact surfaces is taken into account. The evolution of the bonding field is described by a first order differential equation. We derive a variational formulation for the model, in the form of a system for the displacements, the electric potential and the adhesion. Under a smallness assumption which involves only the electrical data of the problem, we prove the existence of a unique weak solution of the model. The proof is based on arguments of time-dependent quasi-variational inequalities, differential equations and Banach's fixed point theorem.

• Proceedings of the Korea Inteligent Information System Society Conference
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• 2005.05a
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• pp.283-291
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• 2005

The development of mobile applications is fast in recent years. However, nearly all applications are for messaging, financial, locating services based on simple interactions with mobile users because of the limited screen size, narrow network bandwidth, and low computing power. Processing an algorithm for supporting a group decision process on mobile devices becomes impossible. In this paper, we introduce the mobile-oriented simple interactive procedure for support a group decision making process. The interactive procedure is developed for multiple objective linear programming problems to help the group select a compromising solution in the mobile Internet environment. Our procedure lessens the burden of group decision makers, which is one of necessary conditions of the mobile environment. Only the partial weak order preferences of variables and objectives from group decision makers are enough for searching the best compromising solution. The methodology is designed to avoid any assumption about the shape or existence of the decision makers's utility function. For the purpose of the experimental study of the procedure, we developed a group decision support system in the mobile Internet environment, MOBIGSS　and applied to an allocation problem of investor assets.

• Journal of the Korean Mathematical Society
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• v.58 no.4
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• pp.873-894
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• 2021

In this paper, we consider the Gudnason model of 𝒩 = 2 supersymmetric field theory, where the gauge field dynamics is governed by two Chern-Simons terms. Recently, it was shown by Han et al. that for a prescribed configuration of vortex points, there exist at least two distinct solutions for the Gudnason model in a flat two-torus, where a sufficient condition was obtained for the existence. Furthermore, one of these solutions has the asymptotic behavior of topological type. In this paper, we prove that such doubly periodic topological solutions are uniquely determined by the location of their vortex points in a weak-coupling regime.

• Bulletin of the Korean Mathematical Society
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• v.57 no.5
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• pp.1269-1297
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• 2020

In this paper, we consider a two-species parabolic-parabolic-elliptic chemotaxis system with weak competition and a fractional diffusion of order s ∈ (0, 2). It is proved that for s > 2p₀, where p₀ is a nonnegative constant depending on the system's parameters, there admits a global classical solution. Apart from this, under the circumstance of small chemotactic strengths, we arrive at the global asymptotic stability of the coexistence steady state.

• The Pure and Applied Mathematics
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• v.24 no.4
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• pp.201-209
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• 2017

We prove convergence properties of the global solutions to the cooperative cross-diffusion system with the intra-specific cooperative pressures dominated by the inter-specific competition pressures and the inter-specific cooperative pressures dominated by intra-specific competition pressures. Under these conditions the $W^1_2-bound$ and the time global existence of the solution for the cooperative cross-diffusion system have been obtained in [10]. In the present paper the convergence of the global solution is established for the cooperative cross-diffusion system with large diffusion coefficients.

• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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• pp.709-730
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• 2022

We consider the nonlinear matrix equation (NMEs) of the form 𝓤 = 𝓠 + Σ^k_i=1 𝓐^*_iℏ(𝓤)𝓐_i, where 𝓠 is n × n Hermitian positive definite matrices (HPDS), 𝓐₁, 𝓐₂, . . . , 𝓐_m are n × n matrices, and ~ is a nonlinear self-mappings of the set of all Hermitian matrices which are continuous in the trace norm. We discuss a sufficient condition ensuring the existence of a unique positive definite solution of a given NME and demonstrate this sufficient condition for a NME 𝓤 = 𝓠 + 𝓐^*₁(𝓤²/900)𝓐₁ + 𝓐^*₂(𝓤²/900)𝓐₂ + 𝓐^*₃(𝓤²/900)𝓐₃. In order to do this, we define 𝓕𝓖_w-contractive conditions and derive fixed points results based on aforesaid contractive condition for a mapping in extended Branciari b-metric distance followed by two suitable examples. In addition, we introduce weak well-posed property, weak limit shadowing property and generalized Ulam-Hyers stability in the underlying space and related results.

• Journal of applied mathematics & informatics
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• v.41 no.3
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• pp.487-510
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• 2023

We propose a mathematical model which describes the frictional contact between a piezoelectric body and an electrically conductive foundation. The behavior of the material is described with a linearly electro-viscoelastic constitutive law with long term memory. The mechanical process is dynamic and the electrical conductivity coefficient depends on the total slip rate, the friction is modeled with Tresca's law which the friction bound depends on the total slip rate with taking into account the electrical conductivity of the foundation both. The main results of this paper concern the existence and uniqueness of the weak solution of the model; the proof is based on results for second order evolution variational inequalities with a time-dependent hemivariational inequality in Banach spaces.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.519-530
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• 2008

This paper studies the multi-domain coupled system of one dimensional Arctic temperature field and establishes identification model about the thermodynamic parameters of sea ice (heat storage capacity, density and conductivity) by the so-called output least-square estimate according to the temperature data acquired by a monitor buoy installed in the Arctic ocean. By the optimal control theory, the existence and dependability of weak solution and the identifiability of identification model have been given. Moreover, necessary optimality condition is proposed. Furthermore, the optimal algorithm for the identification model is constructed. By using the optimal thermodynamic parameters of Arctic sea ice, the numerical simulation is implemented, and the numerical results of temperature distribution of Arctic sea ice are demonstrated.