• Honam Mathematical Journal
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• v.44 no.2
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• pp.281-295
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• 2022

This paper deals with the long - time behavior of global bounded solutions for a non-autonomous dispersive-dissipative equation with time-dependent nonlinear damping terms under the null Dirichlet boundary condition. By a new Lyapunov functional and Łojasiewicz-Simon inequality, we show that any global bounded solution converges to a steady state and get the rate of convergence as well, which depends on the decay of the non-autonomous term g(x, t), when damping coefficients are integral positive and positive-negative, respectively.

• Nonlinear Functional Analysis and Applications
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• v.27 no.3
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• pp.679-689
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• 2022

In this paper, we establish sufficient conditions for the existence and uniqueness of solution for a class of initial boundary value problems with Dirichlet condition in regard to a category of fractional-order partial differential equations. The results are established by a method based on the theorem of Lax Milligram.

• Journal of the Korea Computer Graphics Society
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• v.20 no.4
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• pp.9-16
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• 2014

This paper proposes a novel method that couples fluid and deformation/fracture. Our method considers two interaction types: fluid-object interaction and fluid-fluid interaction. In fluid-fluid interaction, we simulate water and smoke separately and blend their velocities in the intersecting region depend on their densities. Our method separates projection process into two steps for each of water and smoke. This reduces the number of grid cells required for projection in order to optimize the number of iterations for convergence and improve stability of the simulation. In water projection step, smoke region regarded as the cells with Dirichlet boundary condition. The smoke projection step solves water region with Neumann boundary condition. To take care of fluid-object interaction, we make use of the fluid pressure to update velocities of the each of the mass points so that the object can deform or fracture. Although our method doesn't provide physically accurate results, the various examples show that our method generate appealing visuals with good performance.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.37 no.11
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• pp.1066-1072
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• 2009

A panel method based on potential flow theory is developed for the steady/unsteady aerodynamic analysis of arbitrary three-dimensional Blended Wing Body aircraft. The panel method uses the piecewise constant source and doublet singularities as a solution. This potential based panel method is founded on the Dirichlet boundary condition and coupled with the time-stepping method. The present method uses the time-stepping loop to simulate the unsteady motion of the aircraft. The present method can solve the three-dimensional flow over the complex bodies with less computing time and provide various aerodynamic derivatives to secure the stability of Blended Wing Body aircraft. That will do much for practical applications such as aerodynamic designs and analysis of aircraft configurations and flight simulation.