• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2008.04a
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• pp.26-28
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• 2008

This paper is to investigate the existence theorem for the semilinear fuzzy integrodifferential equation in ${E_N}$ by using the concept of fuzzy number whose values are normal, convex, upper semicontinuous and compactly supported interval in ${E_N}$. Main tool is successive iteration method.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.16 no.4
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• pp.235-242
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• 2012

In this paper, we investigate a nonlocal semilinear heat equation with homogeneous Dirichlet boundary condition in a bounded domain, and prove that there exist solutions with positive initial energy that blow up in finite time.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.4
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• pp.397-409
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• 2017

In this paper, we investigated the extinction, positivity, and decay estimates of the solutions to the initial-boundary value problem of the semilinear parabolic equation with nonlinear gradient source and interior absorption terms by using the integral norm estimate method. We found that the decay estimates depend on the choices of initial data, coefficients and domain, and the first eigenvalue of the Laplacean operator with homogeneous Dirichlet boundary condition plays an important role in the proofs of main results.

• East Asian mathematical journal
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• v.30 no.3
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• pp.327-334
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• 2014

In this paper, we construct extrapolated expanded mixed finite element approximations to approximate the scalar unknown, its gradient and its flux of semilinear Sobolev equations. To avoid the difficulty of solving the system of nonlinear equations, we use an extrapolated technique in our construction of the approximations. Some numerical examples are used to show the efficiency of our schemes.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.4
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• pp.339-342
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• 2009

In this paper, we investigate the existence and uniqueness of fuzzy solutions for semilinear fuzzy integrodifferential equations using integral contractor. The notion of 'bounded integral contractor', introduced by Altman[1], is weaker than Lipschitz condition.

• Journal of the Korean Institute of Intelligent Systems
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• v.18 no.4
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• pp.543-548
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• 2008

This paper is to investigate the existence theorem for the semilinear fuzzy integrodifferential equation in $E_N$ by using the concept of fuzzy number whose values are normal, convex, upper semicontinuous and compactly supported interval in $E_N$. Main tool is successive iteration method.

• Journal of the Korean Mathematical Society
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• v.44 no.2
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• pp.249-260
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• 2007

By variational methods, we prove the existence of positive solutions of a class of indefinite weight semilinear elliptic boundary value problems on critical Sobolev exponent.

• Communications of the Korean Mathematical Society
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• v.28 no.4
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• pp.751-766
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• 2013

We study the existence and long-time behavior of solutions to the following semilinear degenerate parabolic equation on $\mathbb{R}^N$: $$\frac{{\partial}u}{{\partial}t}-div({\sigma}(x){\nabla}u+{\lambda}u+f(u)=g(x)$$, under a new condition concerning a variable non-negative diffusivity ${\sigma}({\cdot})$. Some essential difficulty caused by the lack of compactness of Sobolev embeddings is overcome here by exploiting the tail-estimates method.

• Kyungpook Mathematical Journal
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• v.59 no.2
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• pp.241-258
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• 2019

In this paper, we deal with the null controllability of semilinear functional integrodifferential control systems under the Lipschitz continuity of nonlinear terms. Moreover, we establish the regularity and a variation of constant formula for solutions of the given control systems in Hilbert spaces.

• Journal of the Korean Mathematical Society
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• v.58 no.5
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• pp.1279-1298
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• 2021

The aim of this paper is to prove the existence of the global attractor of the Cauchy problem for a semilinear degenerate hyperbolic equation involving strongly degenerate elliptic differential operators. The attractor is characterized as the unstable manifold of the set of stationary points, due to the existence of a Lyapunov functional.