• East Asian mathematical journal
• /
• v.16 no.2
• /
• pp.267-275
• /
• 2000

In this paper, we study the duality theory of nonlinear parabolic systems. The main objective is to prove the duality theorem under general conditions within an infinite-dimensional framework. As an application, an example is given.

• 제어로봇시스템학회:학술대회논문집
• /
• 1993.10b
• /
• pp.420-424
• /
• 1993

New conditions for the exponential stability for both linear nonautnomous finite and a class of infinite dimensional systems described by parabolic partial differential equations (PDE's) are derived. The results for the parabolic systems are derived via semigroup approach.

• Journal of the Korean Mathematical Society
• /
• v.54 no.6
• /
• pp.1817-1828
• /
• 2017

We give a simple and direct proof of the characterization of positivity preserving semi-flows for ordinary differential systems. The same method provides an abstract result on a class of evolution systems containing reaction-diffusion systems in a bounded domain of ${\mathbb{R}}^n$ with either Neumann or Dirichlet homogeneous boundary conditions. The conditions are exactly the same with or without diffusion. A similar approach gives the optimal result for invariant rectangles in the case of Neumann conditions.

• Journal of Mechanical Science and Technology
• /
• v.14 no.2
• /
• pp.168-176
• /
• 2000

Related to the error dynamics of an adaptive system, averaging theorems are developed for coupled differential equations which consist of ordinary differential equations and a parabolic partial differential equation. The results are then applied to the convergence analysis of the parameter estimate errors in the model reference adaptive control of a nonautonomous parabolic partial differential equation with lowly time-varying parameters.

• Journal of the Korean Solar Energy Society
• /
• v.37 no.1
• /
• pp.39-45
• /
• 2017

This paper presents the effect of solar collectors on the performance of solar tracking daylighting systems. A series of measurements were made for two different types of solar collectors mounted on double axis solar trackers: Parabolic dish concentrator and Fresnel Lens. Indoor light levels were measured at different locations of an office space (longitude: 126.33 E, latitude 33.45 N) as photo sensors were placed on a task plane 80 cm above the floor. To accurately monitor the applicability of the systems, measurements were performed under clear and overcast sky conditions with the roll-screen (on the south window) in the down position. Comparing the illuminance data, the system with Fresnel lens outperformed that of parabolic dish concentrator. On clear days, the former delivered the light levels of 400~600 lux on the task plane whereas the latter recorded 100~200 lux. Depending on the amount of cloud cover, on overcast days, illuminance readings fluctuated to some extent.

• Smart Structures and Systems
• /
• v.14 no.2
• /
• pp.71-83
• /
• 2014

The purpose of this paper is to investigate the flexible structure of parabolic shell using photostrictive actuators. The analysis is made to know its dynamic behavior and light-induced control forces for coupled parabolic shell. The effects of an actuator location as well as membrane and bending components under the control action have been analyzed considering the approximate spherical model. The parabolic membrane shell accuracy is being mathematically approximated and validated comparing the light induced control forces using approximate equivalent spherical shell model. The parabolic shell with kapton smart material and photostrictive actuators has been used to formulate the governing equation in the transverse direction. The Kirchhoff-Love assumptions are used to obtain the governing equation of shell with actuator. The mechanical membrane forces and bending moments for parabolic thin shell with actuator is used to analyze the dynamic effect. The results show that membrane control action is much more significant than bending control action. Photostrictive actuators oriented along circumferential direction (actuator-2) can give better control effect than actuators placed along longitudinal direction (actuator-1). The slight difference is observed between spherical and parabolic shell for a surface with focal length to the diameter ratio of 1.00 or more than unity. Space applications often have the shape of parabolical shells or shell of revolution, due to their required focusing, aiming, or reflecting performance. The present approach is focused that photostrictive actuators can effectively control the vibration of parabolical membrane shell. Also, the actuator's location plays an important role in defining the control force.

• Korean Journal of Mathematics
• /
• v.17 no.3
• /
• pp.283-291
• /
• 2009

We investigate the existence of multiple solutions (${\xi},{\eta}$) for perturbations of the parabolic system with Dirichlet boundary condition $$(0.1)\;\begin{array}{lcr}{\xi}_t=-L{\xi}+g_1(3{\xi}+{\eta})-s{\phi}_1-h_1(x,t)\;in\;{\Omega}{\times}(0,\;2{\pi}),\\{\eta}_t=-L{\eta}+g_2(3{\xi}+{\eta})-s{\phi}_1-h_2(x,t)\;in\;{\Omega}{\times}(0,\;2{\pi}).\end{array}$$ We show the existence of multiple solutions (${\xi},{\eta}$) for perturbations of the parabolic system when the nonlinearity $g^{\prime}_1,\;g^{\prime}_2$ are bounded and $3g^{\prime}_1(-{\infty})+g^{\prime}_2(-{\infty})<{\lambda}_1,\;{\lambda}_n<3g^{\prime}_1(+{\infty})+g^{\prime}_2(+{\infty})<{\lambda}_{n+1}$.

• 제어로봇시스템학회:학술대회논문집
• /
• 2000.10a
• /
• pp.408-408
• /
• 2000

A parabolic dish concentrator used in a high temperature application of solar energy tracks the sun's movement by two axis sun tracking system. In such a system, sun tracking performance affects the system efficiency directly. Generally the higher the tracking accuracy is, the better the system performance is. A large number of parabolic dish type concentrators has been developed and implemented in the world. However none of them clearly provided a qualitative method of how the accuracy of the sun tracking system can be evaluated. The work presented here is the evaluation of sun tracking performance of parabolic dish concentrator, which follows the sun's movement by the sensor, using computer vision system. We install a camera on the parabolic dish concentrator. While the concentrator follows the sun, sun's images are captured continuously. Then the performance of sun tracking system was evaluated by analyzing the variation of the position of the sun in the images.

• Korean Journal of Mathematics
• /
• v.16 no.4
• /
• pp.553-564
• /
• 2008

We have a concern with the existence of solutions (${\xi},{\eta}$) for perturbations of the parabolic system with Dirichlet boundary condition $$(0.1)\;\begin{array}{lcr}{\xi}_t=-L{\xi}+{\mu}g(3{\xi}+{\eta})-s{\phi}_1-h_1(x,t)\;in\;{\Omega}{\times}(0,2{\pi}),\\{\eta}_t=-L{\eta}+{\nu}g(3{\xi}+{\eta})-s{\phi}_1-h_2(x,t)\;in\;{\Omega}{\times}(0,2{\pi})\end{array}.$$ We prove the uniqueness theorem when the nonlinearity does not cross eigenvalues. We also investigate multiple solutions (${\xi}(x,t),\;{\eta}(x,t)$) for perturbations of the parabolic system with Dirichlet boundary condition when the nonlinearity f' is bounded and $f^{\prime}(-{\infty})<{\lambda}_1,{\lambda}_n<(3{\mu}+{\nu})f^{\prime}(+{\infty})<{\lambda}_{n+1}$.

• Journal of the Korean Mathematical Society
• /
• v.48 no.3
• /
• pp.513-527
• /
• 2011

The paper deals with the degenerate parabolic system with nonlinear boundary flux. By constructing the self-similar supersolution and subsolution, we obtain the critical global existence curve. The critical Fujita curve is conjectured with the aid of some new results.