• Journal of the Chungcheong Mathematical Society
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• v.28 no.1
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• pp.161-172
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• 2015

In this paper, we consider the chemotaxis-haptotaxis model of tumor invasion with the proliferation and tissue re-establishment term in dimensions one and two. We show the global in time existence of a unique classical solution for the the model in two dimensional spatial domain without any restrictions on the coefficients.

• The Pure and Applied Mathematics
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• v.9 no.1
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• pp.19-30
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• 2002

We consider one class of bursting oscillation models, that is square-wave burster. One of the interesting features of these models is that periodic bursting solution need not to be unique or stable for arbitrarily small values of a singular perturbation parameter $\epsilon$. Recent results show that the bursting solution is uniquely determined and stable for most of the ranges of the small parameter $\epsilon$. In this paper, we present a condition of uniqueness and stability of periodic bursting solutions for all sufficiently small values of $\epsilon$ > 0.

• Bulletin of the Korean Mathematical Society
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• v.40 no.4
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• pp.603-611
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• 2003

In this paper we extend the definition of K-positive definite operators from linear to Frechet differentiable operators. Under this setting, we derive from the inverse function theorem a local existence and approximation results corresponding to those of Theorems land 2 of the authors [8], in an arbitrary real Banach space. Furthermore, an asymptotically K-positive definite operator is introduced and a simplified iteration sequence which converges to the unique solution of an asymptotically K-positive definite operator equation is constructed.

• Communications of the Korean Mathematical Society
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• v.29 no.4
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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.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2004.10a
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• pp.31-34
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• 2004

Carbon nanofiber exhibits superior and often unique characteristics of mechanical, electrical chemical and thermal properties. In this study, For improvement of the mechanical properties of composites, carbon nanofiber reinforced hybrid composites was investigated. For the effect of dispersion, The dispersion methods of solution blending and mechanical mixing were used. The mixing of solution blending method was used using ultrasonic. Dispersion of carbon nanofiber was observed by scanning electron microscope (SEM). Mechanical properties were measured by universal testing Machine (UTM).

• Journal of the Korean Mathematical Society
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• v.34 no.3
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• pp.501-503
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• 1997

The existence of a unique local generalized solution for the abstract functional evolution problem of the type $$ (FDE:\phi) x'(t) + A(t, x_t)x(t) \ni G(t, x_t), t \in [0, T], x_0 = \phi $$ in a general Banach spaces is considered. It is shown that $(FDE:\phi)$ could be considered with well-known fixed point theory and recent results for the functional differential equations involving the operator A(t).

• East Asian mathematical journal
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• v.17 no.2
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• pp.265-273
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• 2001

In this paper, we prove that under certain conditions the Ishikawa iterative method with errors converges strongly to the unique solution of the nonlinear strongly accretive operator equation Tx=f. Related results deal with the solution of the equation x+Tx=f. Our results extend and improve the corresponding results of Liu, Childume, Childume-Osilike, Tan-Xu, Deng, Deng-Ding and others.

• East Asian mathematical journal
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• v.24 no.3
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• pp.295-304
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• 2008

We approximate a locally unique solution of a nonlinear operator equation containing a non-differentiable operator in a Banach space setting using Newton's method. Sufficient conditions for the semilocal convergence of Newton's method in this case have been given by several authors using mainly increasing sequences [1]-[6]. Here, we use center as well as Lipschitz conditions and decreasing majorizing sequences to obtain new sufficient convergence conditions weaker than before in many interesting cases. Numerical examples where our results apply to solve equations but earlier ones cannot [2], [5], [6] are also provided in this study.

• Journal of the Korean Ceramic Society
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• v.28 no.12
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• pp.975-980
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• 1991

Chelated titanium alkoxides are hydrolysed showly and stable enough to prepare multicomponent gels of titania without its precipitation due to the fast hydrolysis of Ti alkoxide. The alkoxy groups of chelated titanium alkoxide are hydrolysed as fast as that of titanium alkoxide but the chelating groups are stable even in aqueous solution. The chelating groups showed different rates of hydrolysis in aqueous ammonia solution and water added one. Those rates were monitored with UV-VIS spectrophotometer by using their unique absorption bands before and after hydrolysis.

• Bulletin of the Korean Mathematical Society
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• v.58 no.6
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• pp.1521-1537
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• 2021

In this paper we consider the global well-posedness of compressible magnetohydrodynamic system in ℝ^d with d ≥ 2, in the framework of the critical Besov spaces. We can show that if the initial data, the shear viscosity and the magnetic diffusion coefficient are small comparing with the volume viscosity, then the compressible magnetohydrodynamic system has a unique global solution. Our result improves the previous one by Danchin and Mucha [10] who considered the compressible Navier-Stokes equations.