• Journal of the Korean Mathematical Society
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• v.44 no.3
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• pp.585-603
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• 2007

The author studies the local $H\ddot{o}lder$ convergence of the solution to an evolution equation of p-Ginzburg-Landau type, to the heat flow of the p-harmonic map, when the parameter tends to zero. The convergence is derived by establishing a uniform gradient estimation for the solution of the regularized equation.

• Kyungpook Mathematical Journal
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• v.49 no.2
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• pp.195-202
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• 2009

This paper deals with very weak solutions of the A-harmonic equation $divA(x,{\nabla}u)$ = 0 (*) with the operator $A:{\Omega}{\times}R^n{\rightarrow}R^n$ satisfies some coercivity and controllable growth conditions with Muckenhoupt weight. By using the Hodge decomposition with weight, a regularity property is proved: There exists an integrable exponent $r_1=r_1({\lambda},n,p)$ < p, such that every very weak solution $u{\in}W_{loc}^{1,r}({\Omega},{\omega})$ with $r_1$ < r < p belongs to $W_{loc}^{1,p}({\Omega},{\omega})$. That is, u is a weak solution to (*) in the usual sense.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1461-1466
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• 2010

aSuppose that (M, g) is a complete Riemannian manifold with Ricci curvature bounded below by -K < 0 and (N, $\bar{b}$) is a complete Riemannian manifold with sectional curvature bounded above by a constant $\mu$ > 0. Let u : $M{\times}[0,\;{\infty}]{\rightarrow}B_{\tau}(p)$ is a heat equation for harmonic map. We estimate the energy density of u.

• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1577-1586
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• 2018

In this paper, we prove that if every bounded ${\mathcal{A}}$-harmonic function on a complete Riemannian manifold M is asymptotically constant at infinity of p-nonparabolic ends of M, then each bounded ${\mathcal{A}}$-harmonic function is uniquely determined by the values at infinity of p-nonparabolic ends of M, where ${\mathcal{A}}$ is a nonlinear elliptic operator of type p on M. Furthermore, in this case, every bounded ${\mathcal{A}}$-harmonic function on M has finite energy.

• Kyungpook Mathematical Journal
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• v.47 no.3
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• pp.311-322
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• 2007

This paper deals with space Beltrami system with three characteristic matrices in even dimensions, which can be regarded as a generalization of space Beltrami system with one and two characteristic matrices. It is transformed into a nonhomogeneous $p$-harmonic equation $d^*A(x,df^I)=d^*B(x,Df)$ by using the technique of out differential forms and exterior algebra of matrices. In the process, we only use the uniformly elliptic condition with respect to the characteristic matrices. The Lipschitz type condition, the monotonicity condition and the homogeneous condition of the operator A and the controlled growth condition of the operator B are derived.

• Wind and Structures
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• v.28 no.6
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• pp.347-354
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• 2019

This study provides an approximate analytical solution to the fractional vibration problem of thin plate governing anomalous motion of plate subjected to in-plane loads. The method of variable separable is employed to transform the fractional partial differential equations under consideration into a fractional ordinary differential equation in temporal variable and a bi-harmonic plate equation in spatial variable. The technique of conformable fractional derivative is utilized to solve the resulting fractional differential equation and the approach of finite sine integral transform method is used to solve the accompanying bi-harmonic plate equation. The deflection field which measures the transverse displacement of the plate is expressed in terms of product of Bessel and trigonometric functions via the temporal and spatial variables respectively. The obtained solution reduces to the solution of the free vibration problem of thin plate in literature. This work shows that conformable fractional derivative is an efficient mathematical tool for tracking analytical solution of fractional partial differential equation governing anomalous vibration of thin plates.

• Journal of Magnetics
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• v.8 no.2
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• pp.93-97
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• 2003

For the induction motor and inverter type motor design, prediction and analysis of core loss including higher harmonics have been studied. In this work, we have generated two symmetrical ac minor loop in the fundamental hysteresis loop whose positions are zero induction region and saturation induction region, and we could pre-dict core loss including higher harmonics inductions. using the following modified superposition principle; $P_c(B_0,f_0,B_h,nf_0)=P_c(B_0,f_0)+(n-1)[K_1(B_0)P_{cL}(B_h,nf_0)+(1-k_1(B_0))P_{cH}(B_h,nf_0)].$Using this equation we could also analyze core losses including higher harmonic induction under different maximum magnetic induction, different amplitude of higher harmonic induction with different harmonic frequencies.

• Wind and Structures
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• v.25 no.1
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• pp.25-38
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• 2017

This study investigates the dynamic analysis of a transversely isotropic thin plate. The plate is made of hyperelastic John's material and its constitutive law is obtained by taken the Frechect derivative of the highlighted energy function with respect to the geometry of deformation. The three-dimensional equation governing the motion of the plate is expressed in terms of first Piola-Kirchhoff's stress tensor. In the reduction to an equivalent two-dimensional plate equation, the obtained model generalizes the classical plate equation of motion. It is obtained that the plate under consideration exhibits harmonic force within its planes whereas this force varnishes in the classical plate model. The presence of harmonic forces within the planes of the considered plate increases the natural and resonance frequencies of the plate in free and forced vibrations respectively. Further, the parameter characterizing the transversely isotropic structure of the plate is observed to increase the plate flexural rigidity which in turn increases both the natural and resonance frequencies. Finally, this study reinforces the view that non-classical models of problems in elasticity provide ample opportunity to reveal important phenomena which classical models often fail to apprehend.

• International Journal of Aeronautical and Space Sciences
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• v.14 no.1
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• pp.19-29
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• 2013

This paper deals with the study of buckling, vibration, and parametric instability characteristics in a damaged cross-ply and angle-ply laminated plate like beam under in-plane harmonic loading, using the finite element approach. Damage is modelled using an anisotropic damage formulation, based on the concept of reduction in stiffness. The effect of damage on free vibration and buckling characteristics of a thin plate like beam has been studied. It has been observed that damage shows a strong orthogonality and in general deteriorates the static and dynamic characteristics. For the harmonic type of loading, analysis was carried out on a thin plate like beam by solving the governing differential equation which is of Mathieu-Hill type, using the method of multiple scales (MMS). The effects of damage and its location on dynamic stability characteristics have been presented. The results indicate that, compared to the undamaged plate like beam, heavily damaged beams show steeper deviations in simple and combination resonance characteristics.

• Journal of the Korean Society of Combustion
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• v.15 no.4
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• pp.22-28
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• 2010

The Direct Quadrature Method of Moments (DQMOM) has been presented for the solution of population balance equation in the wide range of the multi-phase flows. This method has the inherently interesting features which can be easily applied to the multi-inner variable equation. In addition, DQMOM is capable of easily coupling the gas phase with the discrete phases while it requires the relatively low computational cost. Soot inception, subsequent aggregation, surface growth and oxidation are described through a population balance model solved with the DQMOM for soot formation. This approach is also able to represent the evolution of the soot particle size distribution. The turbulence-chemistry interaction is represented by the laminar flamelet model together with the presumed PDF approach and the spherical harmonic P-1 approximation is adopted to account for the radiative heat transfer.