• Kyungpook Mathematical Journal
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• v.53 no.1
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• pp.87-98
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• 2013

In this paper, we devoted to study the existence and uniqueness of nonlinear fuzzy neutral integrodifferential equations. Moreover we study the fuzzy solution for the normal, convex, upper semicontinuous, and compactly supported interval fuzzy number. The results are obtained by using the Banach fixed-point theorem. An example is provided to illustrate the theory.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.1
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• pp.16-25
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• 2021

This paper is studied the existence of a solution for the impulsive Cauchy problem involving the Caputo fractional derivative in Banach space by using topological structures. We based on using topological degree method and fixed point theorem with some suitable conditions. Further, some topological properties for the set of solutions are considered. Finally, an example is presented to demonstrate our results.

• Nonlinear Functional Analysis and Applications
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• v.27 no.1
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• pp.83-97
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• 2022

In this paper, we introduce and study generalized mixed operator quasi-equilibrium problems(GMQOEP) in Hausdorff topological vector spaces and prove the existence results for the solution of (GMQOEP) in compact and noncompact settings by employing 1-person game theorems. Moreover, using coercive condition, hemicontinuity of the functions and KKM theorem, we prove new results on the existence of solution for the particular case of (GMQOEP), that is, generalized mixed operator equilibrium problem (GMOEP).

• Bulletin of the Korean Mathematical Society
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• v.59 no.3
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• pp.745-756
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• 2022

We study a nonlinear wave equation on finite connected weighted graphs. Using Rothe's and energy methods, we prove the existence and uniqueness of solution under certain assumption. For linear wave equation on graphs, Lin and Xie [10] obtained the existence and uniqueness of solution. The main novelty of this paper is that the wave equation we considered has the nonlinear damping term |u_t|^p-1·u_t (p > 1).

• Journal of the Korean Mathematical Society
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• v.60 no.3
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• pp.587-618
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• 2023

In this paper, we consider the existence of time periodic solutions for the compressible magneto-micropolar fluids in the whole space ℝ³. In particular, we first solve the problem in a sequence of bounded domains by the topological degree theory. Then we obtain the existence of time periodic solutions in ℝ³ by a limiting process.

• Journal of Applied and Pure Mathematics
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• v.4 no.1_2
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• pp.71-77
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• 2022

This work considers the existence and uniqueness of fuzzy solutions for impulsive abstract partial neutral functional differential systems. To establish the existence and uniqueness, we apply the concept of impulse, semi group theory and suitable fixed point theorem.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.27 no.1
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• pp.23-36
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• 2023

The vector wave equation is widely used in electromagnetic wave analysis. This paper solves the vector wave equation using curl-conforming finite elements. The variational problem is established from Riesz functional based on vector wave equation and the unique existence of weak solution is explored. The edge elements are used in computation and the simulation results are compared with those obtained from a commercial simulator, ANSYS HFSS (high-frequency structure simulator).

• Journal of Advanced Marine Engineering and Technology
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• v.21 no.5
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• pp.535-541
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• 1997

The effect of concentration of each solution( HCI, $H_2SO_4$ and $HNO_3$), scan rate and polished surface condition on the corrosion of AISI 304 Stainless Steel were investigated, utilizing the Method ASTM G5 - 87. It can be concluded that: 1) For the same concentration(i.e. 1N) of each solution the corrosion rate is the highest in HCI and lowest in $HNO_3$. Also, the difference of values of $i_{cirt}$ generated for each solution is significant. 2) As the concentration of the solution $H_2SO_4$ is increased (O.5N, 1N, 2N) the values of $E_{cor}$ $i_{crit}$ and $i_{p}$ are increased. 3) In case of existence of SCN ion of O.OlN, the values of iCTIt and ip generated are approximately 100 times and 1.4 times higher respectively, than in the case of non - existence of $SCN^{-}$. However the existence of $SCN^{-}$ doesn't affect the value of $E_{cor}$ and $E_{p}$. 4) The values of $i_{crit}$ and $i_{p}$ are increased due to the increase of scan rate. But the values of $E_{cor}$ and $E_{p}$ do not depend on the scan rate. 5) The $i_{p}$ value depends greatly on oxygen in the solution, but the changes in values of $E_{cor}$ $i_{crit}$ and $E_{b}$ due to the oxygen are insignificant. 6) If a component is polished using #400, #600 and #800 wet polish paper, the effect of surface condition on variations of values of $i_{crit}$ and $i_{p}$ is slightly significant.

• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.1049-1064
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• 1997

We study the existence and uniqueness of nonnegative singular solution u(x,t) of the semilinear parabolic equation $$ u_t = \Delta u - a \cdot \nabla(u^q) = u^p, $$ defined in the whole space $R^N$ for t > 0, with initial data $M\delta(x)$, a Dirac mass, with M > 0. The exponents p,q are larger than 1 and the direction vector a is assumed to be constant. We here show that a unique singular solution exists for every M > 0 if and only if 1 < q < (N + 1)/(N - 1) and 1 < p < 1 + $(2q^*)$/(N + 1), where $q^* = max{q, (N + 1)/N}$. This result agrees with the earlier one for N = 1. In the proof of this result, we also show that a unique singular solution of a diffusion-convection equation without absorption, $$ u_t = \Delta u - a \cdot \nabla(u^q), $$ exists if and only if 1 < q < (N + 1)/(N - 1).

• East Asian mathematical journal
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• v.24 no.3
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• pp.305-315
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• 2008

The purpose of this paper is to study the existence and uniqueness of the fixed point of uniformly pseudo-contractive operator and the solution of equation with uniformly accretive operator, and to approximate the fixed point and the solution by the Mann iterative sequence in an arbitrary Banach space or an uniformly smooth Banach space respectively. The results presented in this paper show that if X is a real Banach space and A : X $\rightarrow$ X is an uniformly accretive operator and (I-A)X is bounded then A is a mapping onto X when A is continuous or $X^*$ is uniformly convex and A is demicontinuous. Consequently, the corresponding results which depend on the assumptions that the fixed point of operator and solution of the equation are in existence are improved.