• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.393-409
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• 2021

Three common fixed point theorems for weakly compatible mappings satisfying three classes of contractive inequalities of integral type are proved. Three examples are included. The results obtained in this paper extend and improve a few results existing in literature.

• Nonlinear Functional Analysis and Applications
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• v.26 no.3
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• pp.601-610
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• 2021

A convergence theorem for a generalized 𝜑-weakly contractive mapping is proved which satisfy a generalized contraction condition on a complete metrically convex metric space. The result in this paper generalizes the relevant results due to Rhoades [18], Alber and Guerre-Delabriere [1], Khan and Imdad [14], Xue [20] and others. An illustrative example is also furnished in support of our main result.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.12 no.4
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• pp.181-189
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• 2000

A weakly nonlinear mild-slope equation has been derived directly from the continuity equation with the aid of the Galerkin's method. The equation is combined with the momentum equations defined at the mean water level. A single component model has also been obtained in terms of the surface displacement. The linearized form is completely identical with the time-dependent mild-slope equation proposed by Smith and Sprinks(1975). For the verification purposes of the present nonlinear model, the degenerate forms were compared with Airy(1845)'s non-dispersive nonlinear wave equation, classical Boussinesq equation, andsecond¬order permanent Stokes waves. In this study, the present nonlinear wave equations are discretized by the approximate factorization techniques so that a tridiagonal matrix solver is used for each direction. Through the comparison with physical experiments, nonlinear wave model capacity was examined and the overall agreement was obtained.

• International Journal of Naval Architecture and Ocean Engineering
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• v.3 no.1
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• pp.20-26
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• 2011

A weakly nonlinear seakeeping methodology for predicting motions and loads is presented in this paper. This methodology assumes linear radiation and diffraction forces, calculated in the frequency domain, and fully nonlinear Froude-Krylov and hydrostatic forces, evaluated in the time domain. The particular approach employed here allows to overcome numerical problems connected to the determination of the impulse response functions. The procedure is divided into three consecutive steps: evaluation of dynamic sinkage and trim in calm water that can significantly influence the final results, a linear seakeeping analysis in the frequency domain and a weakly nonlinear simulation. The first two steps are performed employing a three-dimensional Rankine panel method. Nonlinear Froude-Krylov and hydrostatic forces are computed in the time domain by pressure integration on the actual wetted surface at each time step. Although nonlinear forces are evaluated into the time domain, the equations of motion are solved in the frequency domain iteratively passing from the frequency to the time domain until convergence. The containership S175 is employed as a test case for evaluating the capability of this methodology to correctly predict the nonlinear behavior related to wave induced motions and loads in head seas; numerical results are compared with experimental data provided in literature.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.5 no.4
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• pp.350-356
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• 1993

We carry out a numerical calculation to understand the nonlinear wave deformation around breakwaters using the Boussinesq equation, which is weakly nonlinear and weakly dispersive shallow water equation. A numerical method based on a finite element scheme and fourth order Runge-Kutta algorithm is employed to investigate the diffraction of incident waves by the breakwater. As a computational model, two-dimensional wave flume is treated. The breakwaters is perpendicular to the side wall of a channel. From the numerical results, the wave deformations according to the change of the length and the thickness of breakwaters are investigated. We also investigate the effect of the nonlinearity by comparing the results with the linear solutions.

• East Asian mathematical journal
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• v.34 no.5
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• pp.633-641
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• 2018

A viscoelastic wave equation in canonical form weakly nonlinear time dependent dissipation and source terms is investigated in this paper. And we establish a general decay result which is not necessarily of exponential or polynomial type.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.16-19
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• 1996

The objective of this paper is to present a new adaptive nonlinear compensation method, which is based upon the Pth-order inverse theory and can be implemented in a systematic way, for weakly nonlinear systems that can be modeled by a Volterra series. In particular, employment of the proposed approach for the linearization of a given nonlinear system leads to the effective elimination of (up to a required order) nonlinearities in the overall system output. To demonstrate the feasibility of the proposed method, simulation results using a satellite communication system model are also provided.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.10a
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• pp.347-354
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• 2004

Using an efficient adjoint variable method, we develop a unified design sensitivity analysis (DSA) method considering both steady state nonlinear heat conduction and geometrical nonlinear elasticity problems. Design sensitivity expressions with respect to thermal conductivity and Young's modulus are derived. Beside the temperature and displacement adjoint equations, another coupled one is defined regarding the obtained adjoint displacement field as the adjoint load in temperature field. The developed DSA method is shown to be very efficient and further extended to a topology design optimization method for the nonlinear weakly coupled thermo-elasticity problems using a density approach.

• Nonlinear Functional Analysis and Applications
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• v.27 no.2
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• pp.363-379
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• 2022

In this paper, we carried out a new numerical approach for solving integral algebraic equations with weakly singular kernels. The novel method is based on the construction of B-spline tight framelets using the unitary and oblique extension principles. Some numerical examples are given to provide further explanation and validation of our method. The result of this study introduces a new technique for solving weakly singular integral algebraic equation and thus in turn will contribute to providing new insight into approximation solutions for integral algebraic equation (IAE).

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.13 no.2
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• pp.149-157
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• 2001

From the weakly nonlinear mild-slope wave equations introduced by Nadaoka et al.(1994, 1997), a set of weakly nonlinear wave equations for rapidly varying topography are derived by including the bottom curvature and slope-squared tenns ignored in the original equations ofNadaoka et al. To solve the linear version of extended wave equations derived in this study one-dimensional finite difference numerical model is con¬structed. The perfonnance of the model is tested for the case of wave reflection from a plane slope with various inclination. The numerical results are compared with the results calculated using other numerical models reported earlier. The comparison shows that the accuracy of the numerical model is improved significantly in comparison with that of the original equations ofNadaoka et al. by including a complete set of bottom curva1w'e and slope¬squared terms for a rapidly varying topography.