Yong Han Kang

Stabilization of the Kirchhoff type wave equation with locally distributed damping

We derive energy decay estimates of the Kirchhoff type wave equation with a localized damping term in a bounded domain. The damping coefficient function may act alive only on a neighborhood of some part of the boundary.

APPROXIMATE CONTROLLABILITY FOR DIFFERENTIAL EQUATIONS WITH QUASI-AUTONOMOUS OPERATORS

The approximate controllability for the nonlinear control sys- tem with nonlinear monotone hemicontinuous and coercive operator is studied. The existence, uniqueness and a variation of solutions of the system are also given.

Control problems for semi-linear retarded integro-differential equations by the Fredholm theory

ABSTRACT In this paper, we deal with the approximate controllability for semi-linear retarded functional integro-differential equations by using the Fredholm theory in Hilbert spaces. We no longer require the compactness of structural operators to obtain the approximate controllability for the nonlinear differential system, but instead we use the theory of interpolation spaces and the regularity of solutions of semi-linear given equations with unbounded principal operators. Finally, based on the properties of general degree theory in infinite dimensional spaces, we investigate the relation between the reachable set of trajectories of the semi-linear retarded functional integro-differential system and that of its corresponding linear system excluded by the nonlinear term.

PERTURBATION RESULTS FOR HYPERBOLIC EVOLUTION SYSTEMS IN HILBERT SPACES

The purpose of this paper is to derive a perturbation theory of evolution systems of the hyperbolic second order hyperbolic equations. We give an example of a partial functional equation as an application of the preceding result in case of the mixed problems for hyperbolic equa- tions of second order with unbounded principal operators.

ORIENTATIONAL STRESS TENSOR OF POLYMER SOLUTION WITH APPLICATIONS TO BLOOD FLOW

Blood circulating efficiently inside the veins and arteries, provides essential nutrients and oxygen to tissues and organs in the entire body. To highlight the fundamental properties of blood and gain insight into the regularizing effect of various formulations, we need to develop mathematical models. In order to do this, first we present the polymer dynamics in terms of an ensemble of Hookean dumbbells with Brownian configuration fields to derive the orientation stress tensor. Then, we describe the continuity and the momentum equations for time-dependent incompressible flow and the Oldroyd-B model. Finally, we present our numerical analysis of the model and give the effect of the orientation stress tensor in a blood vessel. The development of mathematical models and numerical procedures for the approximation of the blood specific flow equations have enabled us to understand the complex behaviors of blood flows inside the vessel.