• 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.

• Proceedings of the Korean Geotechical Society Conference
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• 2008.03a
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• pp.644-655
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• 2008

Conventional hyperbolic model does not satisfactorily predict the overall stress-strain behaviors of various geomaterials. Tatsuoka and Shibuya(1992) suggest the generalized hyperbolic equation(GHE) considering strain dependency and calculated performance is in good agreement with precise triaxial compression test results of stress-strain relations over wide range of strains before peak stress condition in some cases, but GHE model also does not satisfactorily predict stress-strain relations as strain goes on state of peak stress in most cases. For improve a weak point of the GHE, in this study, modified form of generalized hyperbolic equation (MGHE model) is proposed which can predict highly nonlinear stress-strain behavior for various geomaterials from small strain to peak stress condition.

• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.737-737
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• 2000

• Bulletin of the Korean Mathematical Society
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• v.51 no.1
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• pp.13-27
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• 2014

The purpose of this paper is to derive a perturbation theory of evolution systems of the hyperbolic second order hyperbolic equations. We give an example of a partial functional equation as an application of the preceding result in case of the mixed problems for hyperbolic equations of second order with unbounded principal operators.

• The Pure and Applied Mathematics
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• v.5 no.2
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• pp.87-93
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• 1998

Mejia and Minda proved that if a hyperbolic simply connected region $\Omega$ is k-convex, then (equation omitted), $z \in \Omega$. We show that this inequality actually characterizes k-convex regions.

• East Asian mathematical journal
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• v.30 no.5
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• pp.609-616
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• 2014

In this paper we consider hyperbolic equations related to the p-Laplacian with a nonsmooth kernel. By exploiting a suitable implicit time-discretization technique we obtain the existence of global strong solution.

• Kyungpook Mathematical Journal
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• v.47 no.3
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• pp.347-356
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• 2007

In this paper, we shall consider a class of hyperbolic nonlinear differential equations with continuous deviating arguments. Some new sufficient conditions for oscillation of all solutions with two kinds of boundary conditions are obtained.

• Korean Journal of Mathematics
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• v.19 no.2
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• pp.111-127
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• 2011

We prove the uniqueness solvability of the Tricomi problem for the elliptic - hyperbolical equation of the second type by using a new representation of the solution in the generalized class R.

• Journal of Power System Engineering
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• v.3 no.3
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• pp.14-21
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• 1999

The wave nature of heat conduction has been developed in situations involving extreme thermal gradients, very short times, or temperatures near absolute zero. Under the excitation of a periodic surface heating in a finite medium, the hyperbolic and parabolic heat conduction equations and the damped wave equations in heat flux are presented for comparative analysis by using the Green's function with the integral transform technique. The Kummer transformation is also utilized to accelerate the rate of convergence of these solutions. On the other hand, the temperature distributions are obtained through integration of the energy conservation law with respect to time. For hyperbolic heat conduction, the heat flux distribution does not exist throughout all the region in a finite medium within the range of very short times(${\xi}<{\eta}_l$). It is shown that due to the thermal relaxation time, the hyperbolic heat conduction equation has thermal wave characteristics as the damped wave equation has wave nature.

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1597-1612
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• 2016

There are fruitful results on degenerate parabolic-hyperbolic equations recently following the idea of $Kru{\check{z}}kov^{\prime}s$ doubling variables device. This paper is devoted to the well-posedness of nonhomogeneous boundary problem for degenerate parabolic-hyperbolic equations with spatially dependent second order operator, which has not caused much attention. The novelty is that we use the boundary flux triple instead of boundary layer to treat this problem.