• 제목/요약/키워드: parabolic equation

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LEAST-SQUARES SPECTRAL COLLOCATION PARALLEL METHODS FOR PARABOLIC PROBLEMS

  • SEO, JEONG-KWEON;SHIN, BYEONG-CHUN
    • 호남수학학술지
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    • 제37권3호
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    • pp.299-315
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    • 2015
  • In this paper, we study the first-order system least-squares (FOSLS) spectral method for parabolic partial differential equations. There were lots of least-squares approaches to solve elliptic partial differential equations using finite element approximation. Also, some approaches using spectral methods have been studied in recent. In order to solve the parabolic partial differential equations in parallel, we consider a parallel numerical method based on a hybrid method of the frequency-domain method and first-order system least-squares method. First, we transform the parabolic problem in the space-time domain to the elliptic problems in the space-frequency domain. Second, we solve each elliptic problem in parallel for some frequencies using the first-order system least-squares method. And then we take the discrete inverse Fourier transforms in order to obtain the approximate solution in the space-time domain. We will introduce such a hybrid method and then present a numerical experiment.

자연하천의 연직방향 유속분포 추정을 위한 포물선식 (Quadratic Parabolic Equation to Estimate the Vertical Velocity Distribution in the Natural Streamflow)

  • 박승기;김태철
    • 한국수자원학회논문집
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    • 제33권2호
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    • pp.169-179
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    • 2000
  • 이 연구에서는 1995년부터 1997년까지 금강수계 강경지점에서 유속계로 측정한 유속자료를 분석하여 자연하천의 연직방향 유속분포특성을 규명하였다. 또한, 현장유속 측정조건이 불량하여 다점법으로 유속분포를 측정하기 곤란한 경우, 간단하게 표면유속만을 측정하여 상대깊이별 유속을 추정할 수 있는 연직 유속분포식을 유도하였다. 2차 포물선의 유속분포식은 통계적으로 매우 안정적이고, 표면유속과 바닥유속 등과 고도의 유의성을 보였다. 2차 포물선식의 상수 및 계수와 표면유속과의 상관관계를 구하였으며, 실측 검정자료에 적용한 결과, 유속분포특성을 잘 반영하는 것을 확인할 수 있었다. 연직 유속분포식으로 추정된 유속은 실제수심을 적용하여 평균유속과 유량을 결정할 수 있으며, 이는 또한 하천의 오염물질이동 등 수질해석에 적용할 수 있을 것이다.

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SINGULAR SOLUTIONS OF SEMILINEAR PARABOLIC EQUATIONS IN SEVERAL SPACE DIMENSIONS

  • Baek, Jeong-Seon;Kwak, Min-Kyu
    • 대한수학회지
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    • 제34권4호
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    • pp.1049-1064
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    • 1997
  • We study the existence and uniqueness of nonnegative singular solution u(x,t) of the semilinear parabolic equation $$ u_t = \Delta u - a \cdot \nabla(u^q) = u^p, $$ defined in the whole space $R^N$ for t > 0, with initial data $M\delta(x)$, a Dirac mass, with M > 0. The exponents p,q are larger than 1 and the direction vector a is assumed to be constant. We here show that a unique singular solution exists for every M > 0 if and only if 1 < q < (N + 1)/(N - 1) and 1 < p < 1 + $(2q^*)$/(N + 1), where $q^* = max{q, (N + 1)/N}$. This result agrees with the earlier one for N = 1. In the proof of this result, we also show that a unique singular solution of a diffusion-convection equation without absorption, $$ u_t = \Delta u - a \cdot \nabla(u^q), $$ exists if and only if 1 < q < (N + 1)/(N - 1).

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ON EVOLUTION OF FINSLER RICCI SCALAR

  • Bidabad, Behroz;Sedaghat, Maral Khadem
    • 대한수학회지
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    • 제55권3호
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    • pp.749-761
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    • 2018
  • Here, we calculate the evolution equation of the reduced hh-curvature and the Ricci scalar along the Finslerian Ricci flow. We prove that Finsler Ricci flow preserves positivity of the reduced hh-curvature on finite time. Next, it is shown that evolution of Ricci scalar is a parabolic-type equation and moreover if the initial Finsler metric is of positive flag curvature, then the flag curvature, as well as the Ricci scalar, remain positive as long as the solution exists. Finally, we present a lower bound for Ricci scalar along Ricci flow.

Post-buckling Behavior of Tapered Columns under a Combined Load using Differential Transformation

  • Yoo, Yeong Chan
    • Architectural research
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    • 제8권1호
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    • pp.47-56
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    • 2006
  • In this research, the analysis of post-buckling behavior of tapered columns has been performed under a combined load of uniformly distributed axial load along the length and concentric axial load at free end by solving the nonlinear differential equation with the differential transformation technique. The buckling load at various slopes at free end of column is calculated and the results of the analysis using the differential transformation technique is verified with those of previous studies. It is also shown through the results that the buckling load of sinusoidal tapered columns is largest, the linear is second largest, and the parabolic is small in the all ranges of slopes at free end and the deflection of parabolic tapered columns in the x coordinates is largest, the sinusoidal is second largest, and the linear is smallest in the range of slope 0 to 140 degrees at free end. However, when the range of the slope is 160 to 176 degrees at the free end, the deflection of sinusoidal tapered columns in the x coordinates is largest, the linear is second largest, and the parabolic is smallest. In addition, for the linear tapered column, the buckling load increases along with the flexural stiffness ratio. Also, for the parabolic and the sinusoidal tapered column, the buckling loads increase and decrease as the flexural ratios increase in the range of flexural stiffness ratio n = 1.0 to n = 2.0. Through this research, it is verified that the differential transformation technique can be applied to solve the nonlinear differential equation problems, such as analysis of post-buckling behavior of tapered columns. It is also expected that the differential transformation technique apply to various more complicated problems in future.

일정체적을 갖는 포물선형 중공 보-기둥의 자유진동 해석 (Free Vibration Analysis of Parabolic Hollowed Beam-columns with Constant Volume)

  • 이태은;이병구
    • 한국소음진동공학회논문집
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    • 제21권4호
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    • pp.384-391
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    • 2011
  • This paper deals with free vibrations of the parabolic hollowed beam-columns with constant volume. The cross sections of beam-column taper are the hollowed regular polygons whose depths are varied with the parabolic functional fashion. Volumes of the objective beam-columns are always held constant regardless given geometrical conditions. Ordinary differential equation governing free vibrations of such beam-columns are derived and solved numerically for determining the natural frequencies. In the numerical examples, hinged-hinged, hinged-clamped and clamped-clamped end constraints are considered. As the numerical results, the relationships between non-dimensional frequency parameters and various beam-column parameters such as end constraints, side number, section ratio, thickness ratio and axial load are reported in tables and figures.

Thermal buckling of FGM beams having parabolic thickness variation and temperature dependent materials

  • Arioui, Othman;Belakhdar, Khalil;Kaci, Abdelhakim;Tounsi, Abdelouahed
    • Steel and Composite Structures
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    • 제27권6호
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    • pp.777-788
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    • 2018
  • An investigation on the thermal buckling resistance of simply supported FGM beams having parabolic-concave thickness variation and temperature dependent material properties is presented in this paper. An analytical formulation based on the first order beam theory is derived and the governing differential equation of thermal stability is solved numerically using finite difference method. a function of thickness variation is introduced which controls the parabolic variation intensity of the beam thickness without changing its original material volume. The results showed the high importance of taking into account the temperature-dependent material properties in the thermal buckling analysis of such critical beam sections. Different Influencing parametric on the thermal stability are studied which may help in design guidelines of such complex structures.

Thermal buckling resistance of simply supported FGM plates with parabolic-concave thickness variation

  • Benlahcen, Fouad;Belakhdar, Khalil;Sellami, Mohammed;Tounsi, Abdelouahed
    • Steel and Composite Structures
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    • 제29권5호
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    • pp.591-602
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    • 2018
  • This research presents an investigation on the thermal buckling resistance of FGM plates having parabolic-concave thickness variation exposed to uniform and gradient temperature change. An analytical formulation is derived and the governing differential equation of thermal stability is solved numerically using finite difference method. A specific function of thickness variation is introduced where it controls the parabolic variation intensity of the thickness without changing the original material volume. The results indicated that the loss ratio in buckling resistance is the same for any gradient temperature profile. Influencing geometrical and material parameters on the loss ratio in the thermal resistance buckling are investigated which may help in design guidelines of such complex structures.