• Nonlinear Functional Analysis and Applications
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• 제26권4호
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• pp.839-853
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• 2021

Let 𝕽ⁿ be an Euclidean space and g : 𝕽ⁿ → 𝕽ⁿ be a monotone and continuous mapping. Suppose the convex constrained nonlinear monotone equation problem x ∈ 𝕮 s.t g(x) = 0 has a solution. In this paper, we construct an inertial-type algorithm based on the three-term derivative-free projection method (TTMDY) for convex constrained monotone nonlinear equations. Under some standard assumptions, we establish its global convergence to a solution of the convex constrained nonlinear monotone equation. Furthermore, the proposed algorithm converges much faster than the existing non-inertial algorithm (TTMDY) for convex constrained monotone equations.

• 전기의세계
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• 제30권4호
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• pp.219-226
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• 1981

The magnetic field distribution in saturable iron part of electromagnetic energy conversion divices is defined by the nonlinear quasi-Poisson enquation that is described the electromagnetic field characteristics and satisfied the natural boundary condition. The solution of this equation is obtained by minimizing an energy functional by means of trial function that defined in triangular subregion of two-dimensional field region. As a result, the accuracy of the machine design is increased by use of its solution. In this respect, this study is developed the basic theory to analyze the magnetic flux distribution in saturable iron part and air gap of induction motor that its secondary part is short circuit by the variational principle, the minimized theory of energy functional, the application of F.E.M., and treatment of computer. As theoritical data compared with the practics, the validity of the theory in this study is supported by experimental findings.

• 대한수학회보
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• 제56권1호
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• pp.265-276
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• 2019

For a simple implementation, a linear convex splitting scheme was coupled with the Fourier spectral method for the Cahn-Hilliard equation with a logarithmic free energy. However, an inappropriate value of the splitting parameter of the linear scheme may lead to incorrect morphologies in the phase separation process. In order to overcome this problem, we present a nonlinear convex splitting Fourier spectral scheme for the Cahn-Hilliard equation with a logarithmic free energy, which is an appropriate extension of Eyre's idea of convex-concave decomposition of the energy functional. Using the nonlinear scheme, we derive a useful formula for the relation between the gradient energy coefficient and the thickness of the interfacial layer. And we present numerical simulations showing the different evolution of the solution using the linear and nonlinear schemes. The numerical results demonstrate that the nonlinear scheme is more accurate than the linear one.

• Journal of applied mathematics & informatics
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• 제40권3_4호
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• pp.393-407
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• 2022

In this paper, a diffusive predator-prey system with Beddington DeAngelis functional response and the modified Leslie-Gower type predator dynamics when a prey population is infected is considered. The predator is assumed to predate both the susceptible prey and infected prey following the Beddington-DeAngelis functional response and Holling type II functional response, respectively. The predator follows the modified Leslie-Gower predator dynamics. Both the prey, susceptible and infected, and predator are assumed to be distributed in-homogeneous in space. A reaction-diffusion equation with Neumann boundary conditions is considered to capture the dynamics of the prey and predator population. The global attractor and persistence properties of the system are studied. The priori estimates of the non-constant positive steady state of the system are obtained. The existence of non-constant positive steady state of the system is investigated by the use of Leray-Schauder Theorem. The existence of non-constant positive steady state of the system, with large diffusivity, guarantees for the occurrence of interesting Turing patterns.

• 대한수학회논문집
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• 제36권2호
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• pp.343-359
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• 2021

The aim of this paper is to obtain the general solution of the 2-variable radical functional equations $f({\sqrt[k]{x^k+z^k}},\;{\sqrt[{\ell}]{y^{\ell}+w^{\ell}}})=f(x,y)+f(z,w)$, x, y, z, w ∈ ℝ, for f a mapping from the set of all real numbers ℝ into a vector space, where k and ℓ are fixed positive integers. Also using the fixed point result of Brzdęk and Ciepliński [11, Theorem 1] in (2, 𝛽)-Banach spaces, we prove the generalized hyperstability results of the 2-variable radical functional equations. In the end of this paper we derive some consequences from our main results.

• Journal of applied mathematics & informatics
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• 제7권3호
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• pp.787-800
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• 2000

In this paper we consider an optimal control system described by n-dimensional heat equation with a thermal source. Thus problem is to find an optimal control which puts the system in a finite time T, into a stationary regime and to minimize a general objective function. Here we assume there is no constraints on control. This problem is reduced to a moment problem. We modify the moment problem into one consisting of the minimization of a positive linear functional over a set of Radon measures and we show that there is an optimal measure corresponding to the optimal control. The above optimal measure approximated by a finite combination of atomic measures. This construction gives rise to a finite dimensional linear programming problem, where its solution can be used to determine the optimal combination of atomic measures. Then by using the solution of the above linear programming problem we find a piecewise-constant optimal control function which is an approximate control for the original optimal control problem. Finally we obtain piecewise-constant optimal control for two examples of heat equations with a thermal source in one-dimensional.

• 호남수학학술지
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• 제44권2호
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• pp.281-295
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• 2022

This paper deals with the long - time behavior of global bounded solutions for a non-autonomous dispersive-dissipative equation with time-dependent nonlinear damping terms under the null Dirichlet boundary condition. By a new Lyapunov functional and Łojasiewicz-Simon inequality, we show that any global bounded solution converges to a steady state and get the rate of convergence as well, which depends on the decay of the non-autonomous term g(x, t), when damping coefficients are integral positive and positive-negative, respectively.

• Kyungpook Mathematical Journal
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• 제56권3호
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• pp.831-844
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• 2016

In this paper, we consider a discrete predator-prey system with Watt-type functional response and impulsive controls. First, we find sufficient conditions for stability of a prey-free positive periodic solution of the system by using the Floquet theory and then prove the boundedness of the system. In addition, a condition for the permanence of the system is also obtained. Finally, we illustrate some numerical examples to substantiate our theoretical results, and display bifurcation diagrams and trajectories of some solutions of the system via numerical simulations, which show that impulsive controls can give rise to various kinds of dynamic behaviors.

• Korean Journal of Mathematics
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• 제17권4호
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• pp.419-428
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• 2009

We show the existence of at least one nontrivial solution of the homogeneous mixed type nonlinear elliptic problem. Here mixed type nonlinearity means that the nonlinear part contain the jumping nonlinearity and the critical growth nonlinearity. We first investigate the sub-level sets of the corresponding functional in the Soboles space and the linking inequalities of the functional on the sub-level sets. We next investigate that the functional I satisfies the mountain pass geometry in the critical point theory. We obtain the result by the mountain pass method, the critical point theory and variational method.

• Journal of applied mathematics & informatics
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• 제35권5_6호
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• pp.439-447
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• 2017

This paper investigates the inverse problem of determining an unknown heat radiative coefficient, which is only time-dependent. This is an ill-posed problem, that is, small errors in data may cause huge deviations in determining solution. In this paper, the existence and uniqueness of the problem is established by the second Volterra integral equation theory, and the method of trace-type functional formulation combined with finite difference scheme is studied. One typical numerical example using the proposed method is illustrated and discussed.