• Communications of the Korean Mathematical Society
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• v.12 no.4
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• pp.921-933
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• 1997

An Ambrosetti-Prodi type multiplicity result for periodic-Dirichlet problem to semilinear parabolic equation is treated.

• Journal of the Korean Mathematical Society
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• v.46 no.4
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• pp.691-699
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• 2009

In this paper, we establish a multiple existence result of T-periodic solutions for the semilinear parabolic boundary value problem with sublinear growth nonlinearities. We adapt sub-supersolution scheme and topological argument based on variational structure of functionals.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.33-55
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• 2005

The temporal discretisation of a moderate semilinear parabolic problem in an abstract setting by the two-step backward differentiation formula with variable step sizes is analysed. Stability as well as optimal smooth data error estimates are derived if the ratios of adjacent step sizes are bounded from above by 1.91.

• Journal of the Korean Mathematical Society
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• v.51 no.2
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• pp.267-288
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• 2014

We propose and analyze two-scale product approximation for semilinear heat equations in the mixed finite element method. In order to efficiently resolve nonlinear algebraic equations resulting from the mixed method for semilinear parabolic problems, we treat the nonlinear terms using some interpolation operator and exploit a two-scale grid algorithm. With this scheme, the nonlinear problem is reduced to a linear problem on a fine scale mesh without losing overall accuracy of the final system. We derive optimal order $L^{\infty}((0, T];L^2({\Omega}))$-error estimates for the relevant variables. Numerical results are presented to support the theory developed in this paper.

• 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.

• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.793-803
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• 2000

An impulsive semilinear parabolic equation subject to Robin boundary condition is considered. We prove that for certain classes of impulsive sources and continuous initial data, the solutions of the problem under consideration blow up in the desired time interval.

• East Asian mathematical journal
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• v.35 no.5
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• pp.535-545
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• 2019

This paper is concerned with the optimal control problem associated to strong solution of Belousov-Zhabotinskii reaction model in 2D domain. That is, we otain the global existence of strong solution and show the existence of optimal control.