• Kyungpook Mathematical Journal
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• 제48권1호
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• pp.101-108
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• 2008

In this paper we study the existence of global small solutions of the Cauchy problem for the non-isotropically perturbed nonlinear Schr$\"{o}$dinger equation: $iu_t\;+\;{\Delta}u\;+\;{\mid}u{\mid}^{\alpha}u\;+\;a{\Sigma}_i^d\;u_{x_ix_ix_ix_i}$ = 0, where a is real constant, 1 $\leq$ d < n is a integer is a positive constant, and x = $(x_1,x_2,\cdots,x_n)\;\in\;R^n$. For some admissible ${\alpha}$ we show the existence of global(almost global) solutions and we calculate the regularity of those solutions.

• 대한수학회보
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• 제51권6호
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• pp.1697-1710
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• 2014

The initial-boundary value problem for a class of nonlinear higher-order wave equations system with a damping and source terms in bounded domain is studied. We prove the existence of global solutions. Meanwhile, under the condition of the positive initial energy, it is showed that the solutions blow up in the finite time and the lifespan estimate of solutions is also given.

• 대한수학회지
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• 제34권3호
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• pp.623-632
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• 1997

In this paper, the nonexistence of the global solutions of semilinear wave equations with damping terms in the boundary conditions is investigated.

• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.269-282
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• 2005

We study the global asymptotic stability, global attractivity, boundedness character, and periodic nature of all positive solutions and all negative solutions of the difference equation $$x_{n+1}\;=\;{\alpha}-{\frac{x_{n-1}}{x_{n}},\;n=0,1,\;{\cdots}$$, where ${\alpha}\;\in\; R$ is a real number, and the initial conditions $x_{-1},\;x_0$ are arbitrary real numbers.

• 대한수학회보
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• 제55권2호
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• pp.591-598
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• 2018

This paper is concerned with global existence of weak solutions to the relativistic Vlasov-Klein-Gordon system. The energy of this system is conserved, but the interaction term ${\int}_{{\mathbb{R}}^n}\;{\rho}{\varphi}dx$ in it need not be positive. So far existence of global weak solutions has been established only for small initial data [9, 14]. In two dimensions, this paper shows that the interaction term can be estimated by the kinetic energy to the power of ${\frac{4q-4}{3q-2}}$ for 1 < q < 2. As a consequence, global existence of weak solutions for general initial data is obtained.

• Kyungpook Mathematical Journal
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• 제59권4호
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• pp.631-649
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• 2019

In this paper, we prove the global nonexistence of solutions for a quasilinear wave equation with time delay and acoustic boundary conditions. Further, we establish the blow up result under suitable conditions.

• 대한수학회논문집
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• 제29권4호
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• pp.505-518
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• 2014

Considered here is the first initial boundary value problem for the two-dimensional g-Navier-Stokes equations in bounded domains. We first study the long-time behavior of strong solutions to the problem in term of the existence of a global attractor and global stability of a unique stationary solution. Then we study the long-time finite dimensional approximation of the strong solutions.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제22권1호
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• pp.75-90
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• 2015

In this paper the existence of global solutions of the parabolic cross-diffusion systems with cooperative reactions is obtained under certain conditions. The uniform boundedness of $W_{1,2}$ norms of the local maximal solution is obtained by using interpolation inequalities and comparison results on differential inequalities.

• 대한수학회보
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• 제58권3호
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• pp.729-744
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• 2021

In this paper we prove global existence and uniqueness of axisymmetric strong solutions for the three dimensional electro-hydrodynamic model based on the coupled Navier-Stokes-Poisson-Nernst-Planck system in the exterior of a cylinder. The key ingredient is that we use the axisymmetry of functions to derive the L^p interpolation inequalities, which allows us to establish all kinds of a priori estimates for the velocity field and charged particles via several cancellation laws.

• 대한수학회보
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• 제50권1호
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• pp.275-283
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• 2013

In this paper we investigate an initial boundary value problem of a logarithmic wave equation. We establish the global existence of weak solutions to the problem by using Galerkin method, logarithmic Sobolev inequality and compactness theorem.