• Proceedings of the Korean Society of Marine Engineers Conference
• /
• 2001.05a
• /
• pp.95-99
• /
• 2001

As a way to use energy effectively, the present study is aimed at investigating the performance characteristics of a Single Effect LiBr/Water Absorption Refrigerator using a low temperature driving heat-source. It was carried out by changing the driving heat-source temperature, the cold water outlet temperature(the refrigeration load), the cooling water inlet temperature, and the weak solution flow rate and this study compares the performance characteristics of refrigerator against the existence and non-existence of the Recirculation of the Weak solution which is used as a method to improve the performance of refrigerator. In case of Recirculation of the weak solution, more improved the Refrigeration Capacity and COP was obtained, and these effects became more larger in the high temperature of driving heat-source and large quantity of solution.

• Kyungpook Mathematical Journal
• /
• v.28 no.2
• /
• pp.185-196
• /
• 1988

We study existence of polynomial integrating factors and solutions F(x, y)=c of first order nonlinear differential equations. We characterize the homogeneous case, and give algorithms for finding existence of and a basis for polynomial solutions of linear difference and differential equations and rational solutions or linear differential equations with polynomial coefficients. We relate singularities to nature of the solution. Solution of differential equations in closed form to some degree might be called more an art than a science: The investigator can try a number of methods and for a number of classes of equations these methods always work. In particular integrating factors are tricky to find. An analogous but simpler situation exists for integrating inclosed form, where for instance there exists a criterion for when an exponential integral can be found in closed form. In this paper we make a beginning in several directions on these problems, for 2 variable ordinary differential equations. The case of exact differentials reduces immediately to quadrature. The next step is perhaps that of a polynomial integrating factor, our main study. Here we are able to provide necessary conditions based on related homogeneous equations which probably suffice to decide existence in most cases. As part of our investigations we provide complete algorithms for existence of and finding a basis for polynomial solutions of linear differential and difference equations with polynomial coefficients, also rational solutions for such differential equations. Our goal would be a method for decidability of whether any differential equation Mdx+Mdy=0 with polynomial M, N has algebraic solutions(or an undecidability proof). We reduce the question of all solutions algebraic to singularities but have not yet found a definite procedure to find their type. We begin with general results on the set of all polynomial solutions and integrating factors. Consider a differential equation Mdx+Ndy where M, N are nonreal polynomials in x, y with no common factor. When does there exist an integrating factor u which is (i) polynomial (ii) rational? In case (i) the solution F(x, y)=c will be a polynomial. We assume all functions here are complex analytic polynomial in some open set.

• Kyungpook Mathematical Journal
• /
• v.27 no.1
• /
• pp.43-46
• /
• 1987

In this paper we consider the semilinear hyperbolic symmetric system of the first-order. The existence and uniqueness of the solution are proved, under certain conditions, some properties of the solution are investigated.

• Honam Mathematical Journal
• /
• v.20 no.1
• /
• pp.89-95
• /
• 1998

We show by using some properties of an elliptic integral that certain scalar semilinear elliptic problem has a unique solution.

• The Pure and Applied Mathematics
• /
• v.5 no.1
• /
• pp.33-44
• /
• 1998

This paper is concerned with the existence of mutiple positive solution of (equation omitted) with Dirichlet boundary condition.

• Communications of the Korean Mathematical Society
• /
• v.12 no.3
• /
• pp.655-664
• /
• 1997

The existence and behavior of a bounded solution for a perturbed nonlinear differential equation of the type $$ (DE) x'(t) + Ax(t) \ni G(x(t)), t \in [0, \infty) $$ is considered. First, we consider the existence of a bounded solution with more simple assumptions using the concept of "the method of lines". Then we devote to study its behavior using recent results of almost non-expansive curve which is developed by Djafari Rouhani.i Rouhani.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.2
• /
• pp.589-599
• /
• 2013

In this paper, we propose a sufficient condition for the existence of solutions to general variational inequality problems (GVI(K, F, $g$)). The condition is also necessary when F is a $g-P^M_*$ function. We also investigate the boundedness of the solution set of (GVI(K, F, $g$)). Furthermore, we show that when F is norm-coercive, the general complementarity problems (GCP(K, F, $g$)) has a nonempty compact solution set. Finally, we establish some existence theorems for (GNCP(K, F, $g$)).

• Journal of the Korean Mathematical Society
• /
• v.55 no.3
• /
• pp.531-551
• /
• 2018

In this paper we consider a class of nonlocal parabolic equations in bounded domains with Dirichlet boundary conditions and a new class of nonlinearities. We first prove the existence and uniqueness of weak solutions by using the compactness method. Then we study the existence and fractal dimension estimates of the global attractor for the continuous semigroup generated by the problem. We also prove the existence of stationary solutions and give a sufficient condition for the uniqueness and global exponential stability of the stationary solution. The main novelty of the obtained results is that no restriction is imposed on the upper growth of the nonlinearities.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.3
• /
• pp.753-760
• /
• 2013

We consider the global existence of strong solutions of the 3D incompressible Navier-Stokes equations in a bounded Lipschitz do-main under Dirichlet boundary condition. We present by a very simple argument that a strong solution exists globally when the product of $L^2$ norms of the initial velocity and the gradient of the initial velocity and $L^{p,2}$, $p{\geq}4$ norm of the forcing function are small enough. Our condition is scale invariant and implies many typical known global existence results for small initial data including the sharp dependence of the bound on the volumn of the domain and viscosity. We also present a similar result in the whole domain with slightly stronger condition for the forcing.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.15 no.2
• /
• pp.143-150
• /
• 2011

We consider the global existence of strong solutions of the 3D incompressible Navier-Stokes equations in a thin periodic domain. We present a simple proof that a strong solution exists globally in time when the initial velocity in $H^1$ and the forcing function in $L^p$(0,${\infty}$;$L^2$), $2{\leq}p{\leq}{\infty}$ satisfy certain condition. This condition is basically similar to that by Iftimie and Raugel[7], which covers larger and larger initial data and forcing functions as the thickness of the domain ${\epsilon}$ tends to zero.