• 대한수학회지
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• 제42권2호
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• pp.191-202
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• 2005

A condition on forcing term insuring the multiplicity of Dirichlet-periodic solutions of nonlinear dissipative hyperbolic equations is discussed. The nonlinear term is assumed to have coercive growth.

• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.425-430
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• 2010

In this work, We consider an initial boundary value problem for a class of nonlinear hyperbolic equations. We establish a blow-up result for certain solutions with a dissipative term.

• Kyungpook Mathematical Journal
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• 제56권1호
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• pp.29-40
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• 2016

In this paper, we consider the nonlinear hyperbolic equations with forcing term. Some suffcient conditions for the oscillation are derived by using integral averaging method and a generalized Riccati technique.

• 충청수학회지
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• 제27권1호
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• pp.17-27
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• 2014

In order to study the propagation of singularities for solutions to second order quasilinear strictly hyperbolic equations with boundary, we have to consider the regularity of solutions of first order nonlinear equations satisfied by a characteristic hyper-surface. In this paper, we study the regularity compositions of the form v(${\varphi}$(x), x) with v and ${\varphi}$ assumed to have limited Sobolev regularities and we use it to prove the regularity of solutions of the first order nonlinear equations.

• 대한수학회지
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• 제38권4호
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• pp.843-852
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• 2001

In this lecture I shall discuss some recent progress in the development of methods for attacking the central questions of the formation and structure of singularities and of global regularity for solutions of the Cauchy problem for nonlinear systems of partial differential equations of hyperbolic type. Applications to the Einstein equations of general relativity and to the equations of compressible fluid flow shall be particularly emphasized and detailed.

• Kyungpook Mathematical Journal
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• 제47권3호
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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.

• Journal of applied mathematics & informatics
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• 제2권1호
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• pp.3-10
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• 1995

Nonlinear hyperbolic differenctial equations have been a subject of intense research in the field of gas dynamics due to many engineering problems associated with high-speed airplanes missiles materials processing etc. Recently phenomena known from gas dy-namics are found to occur also in the microeletronic devices such as MOSFET. Here a few interesting mathematical problems are presented along with future areas of research.

• 대한수학회지
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• 제38권4호
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• pp.853-881
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• 2001

Multiplicity for doubly-periodic solutions and Dirichlet-Periodic solutions are treated.

• 대한수학회보
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• 제38권3호
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• pp.505-516
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• 2001

We show the existence and uniqueness of solutions for the Cauchy problem for nonlinear evolution equations with the strong damping: ${\upsilon}"(t)-M(｜{\nablauu}(t)｜^2){\triangle}u(t)-{\delta}{\triangle}u'(t)=f(t)$. As an application, a Kirchhoff model with viscosity is given.

• 호남수학학술지
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• 제35권4호
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• pp.683-699
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• 2013

In this paper, an improved ($\frac{G^{\prime}}{G}$)-expansion method is proposed for obtaining travelling wave solutions of nonlinear evolution equations. The proposed technique called ($\frac{F}{G}$)-expansion method is more powerful than the method ($\frac{G^{\prime}}{G}$)-expansion method. The efficiency of the method is demonstrated on a variety of nonlinear partial differential equations such as KdV equation, mKd equation and Boussinesq equations. As a result, more travelling wave solutions are obtained including not only all the known solutions but also the computation burden is greatly decreased compared with the existing method. The travelling wave solutions are expressed by the hyperbolic functions and the trigonometric functions. The result reveals that the proposed method is simple and effective, and can be used for many other nonlinear evolutions equations arising in mathematical physics.