• Journal of the Korean Mathematical Society
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• v.59 no.1
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• pp.53-69
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• 2022

In this paper, we are concerned with a class of mixed Hessian curvature equations with non-degeneration. By using the maximum principle and constructing an auxiliary function, we obtain the interior gradient estimate of (k - 1)-admissible solutions.

• Journal of the Korean Mathematical Society
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• v.56 no.1
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• pp.91-111
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• 2019

We give a direct proof of the sharp two-sided estimates, recently established in [4, 9], for the Dirichlet heat kernel of the fractional Laplacian with gradient perturbation in $C^{1,1}$ open sets by using Duhamel's formula. We also obtain a gradient estimate for the Dirichlet heat kernel. Our assumption on the open set is slightly weaker in that we only require D to be $C^{1,{\theta}}$ for some ${\theta}{\in}({\alpha}/2,1]$.

• Wind and Structures
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• v.19 no.3
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• pp.249-270
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• 2014

Through comparing the mean wind profiles observed overland during the passages of four typhoons, and the gradient wind speeds calculated based on the sea level pressure data provided by a numerical model, the present paper discusses, (a) whether the gradient balance is a valid assumption to estimate the wind speed in the height range of 1250 m ~ 1750 m, which is defined as the upper-level mean wind speed, in a tropical cyclone over land, and (b) if the super-gradient feature is systematically observed below the height of 1500 m in the tropical cyclone wind field over land. It has been found that, (i) the gradient balance is a valid assumption to estimate the mean upper-level wind speed in tropical cyclones in the radial range from the radius to the maximum wind (RMW) to three times the RMW, (ii) the super-gradient flow dominates the wind field in the tropical cyclone boundary layer inside the RMW and is frequently observed in the radial range from the RMW to twice the RMW, (iii) the gradient wind speed calculated based on the post-landfall sea level pressure data underestimates the overall wind strength at an island site inside the RMW, and (iv) the unsynchronized decay of the pressure and wind fields in the tropical cyclone might be the reason for the underestimation.

• Journal of the Korean Mathematical Society
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• v.57 no.6
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• pp.1509-1533
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• 2020

We provide detailed proofs for local gradient estimates for elliptic equations in divergence form with partial Dini mean oscillation coefficients in a ball and a half ball.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.4
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• pp.397-409
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• 2017

In this paper, we investigated the extinction, positivity, and decay estimates of the solutions to the initial-boundary value problem of the semilinear parabolic equation with nonlinear gradient source and interior absorption terms by using the integral norm estimate method. We found that the decay estimates depend on the choices of initial data, coefficients and domain, and the first eigenvalue of the Laplacean operator with homogeneous Dirichlet boundary condition plays an important role in the proofs of main results.

• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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• pp.853-865
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• 2019

In this paper, we consider gradient estimates for positive solutions to the following nonlinear elliptic equation on a complete Riemannian manifold: $${\Delta}_Vu+cu^{\alpha}=0$$, where c, ${\alpha}$ are two real constants and $c{\neq}0$. By applying Bochner formula and the maximum principle, we obtain local gradient estimates for positive solutions of the above equation on complete Riemannian manifolds with Bakry-${\acute{E}}mery$ Ricci curvature bounded from below, which generalize some results of [8].

• Transactions of the Korean Society of Mechanical Engineers B
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• v.22 no.12
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• pp.1715-1725
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• 1998

A two-dimensional transient inverse heat conduction problem involving the estimation of the unknown location, ($X^*$, $Y^*$), and timewise varying unknown strength, $G({\tau})$, of a line heat source embedded inside a rectangular bar with insulated boundaries has been solved simultaneously. The regular conjugate gradient method, RCGM and the modified conjugate gradient method, MCGM with adjoint equation, are used alternately to estimate the unknown strength $G({\tau})$ of the source term, while the parameter estimation approach is used to estimate the unknown location ($X^*$, $Y^*$) of the line heat source. The alternate use of the regular and the modified conjugate gradient methods alleviates the convergence difficulties encountered at the initial and final times (i.e ${\tau}=0$ and ${\tau}={\tau}_f$), hence stabilizes the computation and fastens the convergence of the solution. In order to examine the effectiveness of this approach under severe test conditions, the unknown strength $G({\tau})$ is chosen in the form of rectangular, triangular and sinusoidal functions.

• Journal of applied mathematics & informatics
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• v.39 no.1_2
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• pp.165-172
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• 2021

We prove a lower estimate of Neumann eigenvalues on compact manifolds with the condition that the Ricci curvature is bounded below. We improved the earlier results.

• Journal of the Korean Mathematical Society
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• v.51 no.6
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• pp.1209-1220
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• 2014

We prove global gradient estimates in weighted Orlicz spaces for weak solutions of nonlinear elliptic equations in divergence form over a bounded non-smooth domain as a generalization of Calder$\acute{o}$n-Zygmund theory. For each point and each small scale, the main assumptions are that nonlinearity is assumed to have a uniformly small mean oscillation and that the boundary of the domain is sufficiently flat.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.5 no.4
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• pp.74-81
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• 1996

This paper is to estimate sizing design sensitivity of linear and nonlinear vehicle frame structure using structural ananlysis result from ANSYS. Using design sensitivity results, optimal design of plane vehicle frame structure with buckling constraint is carried out the gradient projection method. Optimal design results are compares gradient projection method resrult with SUMT result.