• Communications of the Korean Mathematical Society
• /
• v.20 no.3
• /
• pp.589-602
• /
• 2005

We present the numerical algorithm for the model for high-strain rate deformation in hyperelastic-viscoplastic materials based on a fully conservative Eulerian formulation by Plohr and Sharp. We use a hyperelastic equation of state and the modified Steinberg and Lund's rate dependent plasticity model for plasticity. A two-dimensional approximate Riemann solver is constructed in an unsplit manner to resolve the complex wave structure and combined with the second order TVD flux. Numerical results are also presented.

• Journal of applied mathematics & informatics
• /
• v.26 no.1_2
• /
• pp.299-306
• /
• 2008

Finite difference schemes are considered for a $Ca^{2+}$ diffusion equations, which discribe $Ca^{2+}$ buffering by using stationary and mobile buffers. Stability and $L^\infty$ error estimates of approximate solutions for the corresponding schemes are obtained using the extended Lax-Richtmyer equivalence theorem.

• The Pure and Applied Mathematics
• /
• v.17 no.2
• /
• pp.115-130
• /
• 2010

Let $\cal{A}$ be a unital Banach algebra. If f : $\cal{A}{\rightarrow}\cal{A}$ is an approximately quadratic derivation in the sense of Hyers-Ulam-J.M. Rassias, then f : $\cal{A}{\rightarrow}\cal{A}$ is anexactly quadratic derivation. On the other hands, let $\cal{A}$ and $\cal{B}$ be Banach algebras.Any approximately generalized homomorphism f : $\cal{A}{\rightarrow}\cal{B}$ corresponding to Cauchy, Jensen functional equation can be estimated by a generalized homomorphism.

• Communications of the Korean Mathematical Society
• /
• v.28 no.2
• /
• pp.319-333
• /
• 2013

Using the fixed point method, we prove the generalized Hyers-Ulam-Rassias stability of the following functional equation in multi-Banach spaces: $${\sum_{1{\leq}i_<j{\leq}n}}\;f(\frac{r_ix_i+r_jx_j}{k})=\frac{n-1}{k}{\sum_{i=1}^n}r_if(x_i)$$.

• Journal of the Korean Mathematical Society
• /
• v.33 no.2
• /
• pp.291-307
• /
• 1996

In this paper, we shall show the existence of solutions of the following nonlinear partial differential equation $$ {^{divA(-\Delta u) = f(x, u, \Delta u) in \Omega}^{u = 0 on \partial\Omega} $$ where $f(x, u, \Delta u) = -u$\mid$\Delta u$\mid$^{p-2} + h, p \geq 2, h \in L^\infty$.

• Journal of the Korean Mathematical Society
• /
• v.39 no.4
• /
• pp.579-591
• /
• 2002

New fixed Point results for the (equation omitted) selfmaps ale given. The analysis relies on a factorization idea. The notion of an essential map is also introduced for a wide class of maps. Finally, from a new fixed point theorem of ours, we deduce some equilibrium theorems.

• Bulletin of the Korean Mathematical Society
• /
• v.49 no.6
• /
• pp.1179-1192
• /
• 2012

In this paper, we consider a doubly nonlinear parabolic partial differential equation $\frac{{\partial}{\beta}(u)}{{\partial}t}-{\Delta}_pu+f(x,t,u)=0$ in ${\Omega}{\times}[0,T]$, with Dirichlet boundary condition and initial data given. We prove the existence of a discrete approximate solution by means of the Rothe discretization in time method under some conditions on ${\beta}$, $f$ and $p$.

• Journal of The Korean Astronomical Society
• /
• v.42 no.3
• /
• pp.47-54
• /
• 2009

In this paper we present an independent FORTRAN code for calculating LTE-plane-parallel model atmospheres. The transfer equation has been solved using Avrett and Loeser method. It is shown that, using an approximate non-gray temperature distribution together with the iteration factors method (Simonneau and Crivellari) for correcting the temperature distribution reduce the number of iteration required to achieve the condition of radiative equilibrium. Preliminary results for pure helium model atmospheres are presented.

• 제어로봇시스템학회:학술대회논문집
• /
• 1989.10a
• /
• pp.828-834
• /
• 1989

On-Line optimization of process units has heretofore been restricted to the individual equipment level using linear approximate models. The advent of the low cost, high speed micro-computer coupled with the speed and robustness of an equation based exact simulator is making real-time optimization of entire process units a reality. The resultant implications for a decision system applied to day-to-day operations, point to a significant change in the way process plants will be managed in the future.

• Journal of applied mathematics & informatics
• /
• v.15 no.1_2
• /
• pp.343-361
• /
• 2004

We prove the generalized Hyers-Ulam-Rassias stability of cyclic functional equations in Banach modules over a unital $C^{*}$-algebra. It is applied to show the stability of algebra homomorphisms between Banach algebras associated with cyclic functional equations in Banach algebras.